Captain Smooth and Sergeant Rough

"If the crew doesn't hate the XO, then he isn't doing his job."

—Col. Saul Tigh, Battlestar Galactica

This is a type of ensemble, in which the top authority figure rules in a more refined way and the under boss in a more straightforward way. That is, The Captain will be an Officer and a Gentleman and A Father to His Men. When he needs to intimidate he will use subtle means like a Death Glare. By contrast lower level bosses like a Father Neptune, a Sergeant Rock or, if the crew is unlucky, Drill Sergeant Nasty will be harsh and direct in their method of rule.

This is to some degree Truth in Television. Not only is it a holdover from class differences, but it reflects the fundamental difference between the two roles: The officer must concern himself with the big picture, providing direction to his unit in the form of plans and orders, while the NCO's business is in the details, enforcing discipline, maintaining the unit's proficiency, and personally directing his soldiers in battle. It can also be a useful psychological trick that bears relations with Good Cop, Bad Cop.

Readily capable of subversion, as that refined top figure is the boss for a reason and might be very dangerous if his full attention is called for.

Examples of Captain Smooth and Sergeant Rough include:

Anime and Manga

Taki and Klaus of Hyakujitsu no Bara fit this trope, although their positions are more analogous to "colonel" and "captain" respectively. Although Klaus is shown to have a lot of concern for his subordinates in action, he is distastefully viewed by Taki's compatriots as wild and rough-around-the-edges, and he is very frank with orders. In contrast Taki is idolized by his troops who see him as someone who can never do wrong, and the Death Glare is the most he will exercise on his own men. At one point Taki does come closer to the "rough" side however, when he uses training to vent his own frustration, resulting in him ruthlessly beating soldiers (one of whom was already injured) foolish enough to try their luck against him.
Lieutenant Filicia Heideman and Sergeant Rio Kazumiya of So Ra No Wo To.
Shiro Amada and Karen Joshua of Mobile Suit Gundam: The 08th MS Team.
Minna and Mio of Strike Witches are a Wing Commander Smooth and a Lieutenant Commander Rough.

Comic Books

Captain America (comics) occasionally features this during his WWII adventures, with the Sergeant usually being Sgt. Nick Fury, but his first mission featured Bucky as the Sergeant Rough as seen in Wolverine Origins.
The comic version of 300 had a King Smooth and Captain Rough. Leonidas was usually very calm and stoic while his Captain was brutish and violent.

Film

Glory: The commander is an Officer And A Gentleman while the two sergeants are rougher and less refined. One is a Sergeant Rock and the other a Drill Sergeant Nasty.
Zulu In this the sergeant is a fairly good natured fellow, but has an "unpolished" feel to him.
In Top Gun, Tom Skerrit (Viper) and Michael Ironsides (Jester) are Trope Codifiers.
Michael Ironsides gets his chance to be Captain Smooth in Starship Troopers to Clancy Brown's Sgt. Zim who is of course the "sergeant rough".
Optimus Prime and Ironhide in the Transformers Film Series.
In G.I. Jane, Command Master Chief John James Urgayle is Captain Smooth (only once does he ever bark at a trainee), while his two subordinate instructors jointly fill the Sergeant Rough position.
In We Were Soldiers, Lieutenant Colonel Hal Moore and Command Sergeant Major Plumley fit this trope.
Saving Private Ryan's Captain Miller(Tom Hanks) and Sgt. Horvath(Tom Sizemore)
In John Ford's "Cavalry Trilogy" of Fort Apache, She Wore a Yellow Ribbon and Rio Grande John Wayne always plays the commanding officer while Victor McLaglan plays his loyal sergeant.
- Not in Fort Apache, there Henry Fonda is the commanding officer and Ward Bond as the Sergeant-Major comes close to being an Officer and a Gentleman since he served as an officer in the American Civil War. McLaglan is just one of the minor sergeants under Bond, but the one with whom John Wayne goes on a special mission is the former Confederate officer played by Pedro Armendariz.
- In Fort Apache this trope is even somewhat Lampshaded in a scene where the young lieutenant O'Rourke seems embarrassed as he is about to train a platoon of recruits, the sergeants comment that young O'Rourke is a gentleman and training recruits is not a job for a gentleman. And then they take it over.
A non-military example occurs in The Shawshank Redemption, with Warden Norton filling the role of Captain Smooth and Captain Hadley being the Sergeant Rough. These roles are apparent in the dressing-down of the new meat.
At the end of the new Star Trek movie, the roles are flipped.Kirk, a former Jerk with a Heart of Gold and Military Maverick,is in the command chair with cool, collectedSpock as his first officer. Note the original Kirk was not rough around the edges in any sense, but was an Officer and a Gentleman despite sharing certain traits (such as womanizing and hubris) with his AU counterpart.
Although both are officers, Von Ryan's Express has Colonel Ryan and Major Fincham. Ryan is a self-declared "90 Day Wonder" who was drafted in to serve as an Army pilot, earning his rank of colonel due to age and education. Fincham is a major but has lived his whole life as a battlefield soldier, and obsesses over discipline and adhering to a code of behavior that Ryan can't fathom. They clash early and often over every step Ryan implements, with Ryan proved right some times and Fincham proved right (painfully so) at other times.
In The Good, the Bad and the Ugly Blondie(the Good) and Tuco (the Ugly) are captured by Union soldiers and brought to a harsh prison camp (they were both wearing Confederate uniforms at the time and Tuco had foolishly shouted some pro-Confederate remarks just before being captured). There are three officers shown to be running the camp, and the two most prominently shown are the extremely brutal Corporal Wallace and Angel Eyes (the Bad). The commandant is actually a decent guy who tries to get the two brutal officers to treat the prisoners fairly. Unfortunately, he's dying from an infected wound, and unable to stop the two officers from taking prisoners inside a building just so they can beat the crap out of them.
The Departed has another non-military example. Mark Wahlberg's Staff Sergeant Dignam is much more coarse and rough when compared to Martin Sheen's diplomatic Captain Queenan.
Gettysburg—and The Killer Angels, the book it was based on—features Col. Joshua Lawrence Chamberlain and his sergeant Buster Kilroy. Chamberlain is an academic and a professor, Kilroy is a rough, sarcastic, out-and-out career soldier. Between them they keep the 20th Maine up and running for its Crowning Moment of Awesome at Little Round Top.

Literature

Over the Wine Dark Sea: Menedemos, the captain is the Magnetic Hero while Diokles the Father Neptune type oarmaster, bellows at the men. Menedemos even describes to his cousin Sostratos the synergy between his method and that of Diokles.
- Harry Turtledove is fond of this trope in general. Another use is the relationship between refined Roman tribune Marcus Aemilius Scaurus and his Sir Swearsalot centurion Gaius Philippus in the Videssos series.
Horatio Hornblower: In one scene, a bosun beats up a recalcitrant sailor. Hornblower is grateful that he is a Captain and too exalted to do such things as he is probably not a good enough fighter.
- Hornblower and his loyal first officer William Bush fit this trope quite well. Though Bush is in no way unusually rough for his time - it's rather that Hornblower has very modern views about discipline and punishment.
Inverted in the book Ender's Game, and Ender even has a psychological reason for it: mercy and good consequences should come from his troops' immediate commanders, discipline and bad consequences from he, Ender, as the overall commander, mainly so it bonds his squads into tighter units willing to protect each other.
In Robin Hobb's Liveship Traders trilogy, it's mentioned a few times that the captain gives the orders and the first mate beats the men into line when necessary.
In first two novels of The Serpentwar Saga by Raymond Feist, The aloof half-elven Captain Calis with super-human strength and senses, and the rough, foul-mouthed Sergent DeLoungeville are an obvious fit.
In Watership Down Hazel is the Captain Smooth, and Bigwig is the Sergeant Rough. Inverted with their Efrafran counterparts: General Woundwart is a brute who rules by force and Captain Campion is a calm-headed strategist.
The Discworld novel Monstrous Regiment has Lieutenant Blouse as the soft, inexperienced "Rupert" with Sergeant Jackrum as the experienced, conniving, shouty NCO who actually makes the decisions.
The main character of the Codex Alera, Tavi, is the calm, refined, highly intelligent and singularly unpowered captain; his primary lieutenants are the absurdly powerful Boisterous Bruiser Maximus and the cynical, grizzled veteran centurion Valiar Marcus. This is one of the subversions, though—Tavi is probably the most dangerous of the lot, due to a combination of intellect, creativity, training, and sheer Badass audacity.
Tour of the Merrimack has this sort of contrast between John Farragut, the smooth captain of the Merrimack, and TR Steele, the rough colonel who leads its Space Marines.
In the Harry Potter series, headmaster Albus Dumbledore and deputy headmistress Minerva McGonagall fit this pretty well. Dumbledore is the Eccentric Mentor and generally doesn't seem to care much about school rules being enforced. McGonagall is a serious Stern Teacher, although she is occasionally Not So Stoic. In Harry Potter and the Philosopher's Stone, Dumbledore catches Harry out of bed after curfew and his response is to have a nice mentorly talk with him. Later on in the same book, McGonagall catches Harry and friends out after curfew and her response is to dock a shitload of points and give them all detentions.
In Belisarius Series, Belisarius has Valentinian as his personal enforcer. When someone disobeys orders in the middle of a battle or tries to rape civilians afterwords Valentinian handles it very efficiently.

Live-Action TV

Inverted in Dad's Army where Captain Mainwaring is a oafish but brave amateur and Sergeant Wilson is a suave aristocrat with extensive military experience. Mainwaring's (and Wilson's) intense awareness of the class inversion was a comedy goldmine.
- Only in the last episode was it revealed that Wilson was indeed a genuine Regular Army Captain Smooth from the previous war. He was filling in as sergeant so that Mainwaring could be Captain if he wanted to; having been a real captain he had no intention of squabbling over who should be a Home Guard captain at his time of life.
In Andromeda, Hunt is the captain smooth, while Valentine bears some traces of sergeant rough.
In Boston Public, the principal is smooth (shaved head!) and tactful, while the VP is a strict disciplinarian with a knack for intimidating... and the funny thing is that the principal is just a scowl away from being a Scary Black Man, while the VP is a short, slim and normally unremarkable white guy.
In Ultimate Force, Col. Aidan Dempsey (Miles Anderson) is the Captain Smooth, while Ross Kemp's SSGT Henry 'Henno' Garvie fits the Sgt Rough trope to a T.
To a lesser extent, Gustavo and Griffin of Big Time Rush fit this trope. Griffin (who owns the record company) is smooth and collected, while Gustavo (who works under him) yells a lot.
Battlestar Galactica: In the reimagined series, ~~Commander~~ Admiral Adama and Colonel Tigh. Adama knows the name and face of every single member of his crew by heart, has demonstrated that he will go to war over every last one of them, and has a Death Glare with its own page on the Battlestar Wiki. Tigh, on the other hand, openly states in the pilot miniseries "If the crew doesn't hate the XO, he's not doing his job."
Winters and Speirs on Band of Brothers, kind of. Also Truth in Television.
- Inverted in the first episode. Captain Sobel is the Drill Sergeant Nasty while Lieutenant Winters is the nice officer the men like.
Firefly inverts this: Malcolm Reynolds, who keeps his Sergeant Rough from his war days, calls himself a captain. His Lancer, Zoe, is calm, cool, and collected, even when she is about to end you.
Inverted in the remake of Hawaii Five 0. Despite being in charge, Steve is the biggest wildcard on the team and is known for his inventive interrogation techniques, while Danny is much more by-the-book and civilised.
Sharpe and Harper in Sharpe, though Sharpe is somewhat less refined than most officers.
Criminal Minds invokes this trope from time to time, with Aaron Hotchner as Captain Smooth and David Rossi as Sergeant Rough.
Captain Sisko and Major Kira of Star Trek: Deep Space Nine. Sisko is rather more polite and refined about his orders. Kira is not refined, nor does she pretend to be. Her preferred manner of dealing with problems is to yell at them until they go away and/or resolve themselves. If this doesn't work, she resorts to fists.

Radio

In Revolting People, the redcoats are represented by the polite and charming Captain Brimshaw and the obnoxious, cynical Sergeant McGurk.

Video Games

The Circle Tower in Dragon Age Origins is shared by the Circle of Magi and the Templars, with a First Enchanter and a Knight-Commander usually sharing the duties. In the game, Knight-Commander Gregoir is "Rough" and First Enchanter Irving is "Smooth," and the two of them butt heads much more often than one would usually see in this situation. Of course, the fact that the Templars' duties include killing rogue Mages might have something to do with it...
Inverted in Dragon Age 2, Meredith is a lot more hard-line and brutal than her more diplomatic and practical second-in-command Cullen.
In Mass Effect, Paragon Shepard tends to be Captain Smooth towards either Ashley in the first game, or Miranda in the second. Renegade Shepard inverts this, with Kaidan and/or Jacob being the more reasonable subordinate.
In Pokémon Mystery Dungeon Explorers of Time/Darkness/Sky, Guild Leader Wigglytuff and his second-in-command Chatot work as this!
The Cavalry in Final Fantasy XIII are led by the gentlemanly Brigadier General Cid Raines, and his more rough-and-tumble subordinate Rygdea.
- Lightning, being an actual sergeant, literalizes this trope. Her solution to everything is to crack heads open, while her cooler-headed superior officer Amodar suggests she try to stay out of the business of Cocoon's leaders.
From Valkyria Chronicles, we have Captain Varrot (who is Welkin's direct superior and overall commander of the militia) and Largo (whose rank is unspecified but presumably that of an NCO). Formerly squad mates in the previous war, they still maintain a rather tenuous relationship, due to Varrot's inability to get over the death of her lover and Largo's unrequited feelings for her. In the end, she gets over it and settles down with Largo after the war.

Western Animation

Lieutenant J.T. Marsh and his second-in-command Sergeant Rita Torres in Exo Squad probably qualify, though they are less extreme than the usual description. Also, Nara Burns and Torres after Marsh is promoted.
Star Wars the Clone Wars gives us Captain Rex and Commander Cody.
Transformers Animated has Ultra Magnus, a fair and ethical leader for the most part. His second and successor Sentinel Prime is a complete Jerkass who abuses his authority up, down and sideways.
Colonel Grumb and Sergeant Blast from Private Olive Oyl (a feature from the The All-New Popeye Hour).

Real Life

As noted above, this trope largely originates from the time when most of the officers were from aristocratic families, while NCOs were generally low-born grunts who had survived previous campaigns long enough to learn the "tricks of the trade" through personal experience. Today, officers and NCOs go through completely separate training programmes and promotion from one group to the other is rare (as they do different jobs, it's more of a career change than a promotion). In the modern era, it's also fairly common for sergeants to have a higher pay grade than their commanding officer, for this reason.
- Yet it's still an effective chemistry, sometimes invoked a bit, but always lampshaded.
Most American high schools have the vice-principal as the chief enforcer and disciplinarian.
Before Conscription was eliminated in Romania, all newly drafted individuals with a university degree would be enlisted into an academy that would train them into officers. While high ranking officers oversaw the education, the sergeants were still responsible for keeping them disciplined, leading to an inversion of this trope. On graduation day however, the trope would end up being played straight, with the students getting promoted, and outranking the sergeants who had been bossing them around for six months. The sergeants, of course, never participated in such events to avoid the humiliation.
In various parliamentary systems (as in the UK and the US), each party has a leader and a "whip" among its representatives, where the latter's job is to enforce party discipline by (almost) all means.
In many governments (including the UK, Australia, Canada, and other Parliamentary governments - notably excluding the USA), it is common to divide the jobs of ceremonial head of state and workaday head of government. This has its advantages: the first can do the jobs of advertising the state with ceremony and largesse, by performing religious duties, dispensing honors, taking care of national treasures, playing dress up, tossing coins to beggers, whatever; while the second can do the gritty work of politics without its nastiness touching the fine image of the head of state.