Synchronous Episodes

In which two episodes of a series, usually (but not always) right next to each other in broadcast order if they're in a broadcast medium, are shown by overlapping scenes to occur at the same time. Synchronous Episodes at times have subtle differences based on which character is the focus in which episode, relating it to The Rashomon.

Examples of Synchronous Episodes include:

Anime and Manga

K-On! does this in the second season, when the older girls go on a class trip, leaving Azusa behind. The bonus episodes and The Movie all also take place during the the last few episodes of the second season.
The end of episode 22 of My-HiME is synchronous with events within the first few minutes of episode 23, with the former scene of the former repeating about four minutes into the latter.
Persona Trinity Soul uses three repeated scenes to establish episodes 9 and 10 as simultaneous; one follows the main protagonist, while the other follows what the other major characters did during that day.
The entire fourth disk of Wolf's Rain is just four recap episodes, each rehashing the plot up to that point, each from the point of view of a different character.
- There are a few additional or revised scenes, so watching those episodes might not be a complete waste of time...
Episodes of Keroro Gunsou usually have two separate 11-minute stories, but episode 44 involved two concurrent stories. The first story has Keroro and Fuyuki competing in various winter sports while mysterious accidents occur, and the second shows that all the accidents were caused by Aki and Kululu testing out a giant robot.
Episodes 17 and 18 of Rental Magica begin with similar but not identical showings of one set of events... but episode 18 quickly becomes a Lower Deck Episode.

Comic Books

Two issues of Invincible depict Omni-Man telling his son about where he came from. The first time, he'd lied to him, and said his home planet Viltrum was a peaceful place, and that he'd been sent to keep order on Earth. The second time, he told the truth: He's a Galactic Conqueror, just one of millions in the Viltrumite horde. They both show the same setting (scenes on Viltrum share the same characters, but while they were all talking joyfully in the first story, they were fighting for supremacy in the second, etc.). In a neat bit of work with the medium, the second story is shown using basically the same page layouts as the first as well, making the distorted echo effect even more obvious.
Elf Quest does this with two entire subseries, Shards and the latter part of Hidden Years (featuring different characters and locations). The two series don't technically share scenes, but there is a lot of overlap, with characters in the one story learning about what happened to their friends in the other. In the European version, they were published together in extra thick comic books which contained one episode of each, happening simultaneously.

Film

This was the concept of Vantage Point.
Saw 3 and the bulk of 4 are revealed at the end of 4 to occur at the same time, when the protagonist of 4 crashes into the sole survivor of 3.

Literature

The Discworld novel Night Watch starts right in the middle of Thief of Time.

Live-Action TV

The two Lexx episodes "The Web" and "The Net" are particularly ingenious/egregious examples of this. The first episode sets up a mystery that's explained in the second, but in the process roughly 75% of the second episode consists of Stock Footage from the first.
Farscape: "Mental as Anything" was a filler ep that focused on the male characters of the show visiting a psychic boot camp to prepare themselves to take on the Scarrans and their infamous heat torture; simultaneously, the girls of Farscape- including the two female big bads at the time- had a particularly stand-out Day in The Limelight episode called "Bringing Home the Beacon," which involved them infiltrating and attempting to derail a secret negotiation between Scarran and Peacekeeper forces on a commerce planet.
The first few episodes of season 2 of Lost did this, with Jack, Kate, and Locke's entrances into the hatch playing out over the course of three episodes. Other episodes focus on the goings-on at certain parts of the island, with adjacent episodes showing the same time periods in different locales.
- The flashbacks of "House of the Rising Sun" and "...In Translation" are also synchronous. Those episodes aired half a season apart.
- Been happening a lot during Season 5 with its Time Travelling. Specifically in 'The Little Prince' and 'Do No Harm/Deus Ex Machina'. Recently 'Because You Left' and 'Follow the Leader' had the same scene from different perspectives too.
How I Met Your Mother does this a lot, but usually so subtly you don't catch it the first time. The most obvious is in season three with the episode "Ten Sessions" (with references to other episodes that already had or were going to happen during those ten weeks) but a particularly brilliant usage comes at the end of season two when Ted and Robin secretly break up three episodes before the wedding, but decide not to tell anyone until after the wedding. The story of the breakup is told in flashback, but is obviously happening at the same time as a previous episode, with many references back and forth.
- The season 1 episode Life Among the Gorillas ends with Robin giving Ted what amounts to a booty call. The next episode Nothing Good Happens After 2 A.M. starts with showing what she was up to during the previous episode, detailing the emotionally draining day (including coaching Ted on his girlfriend problems) that led to her making that call.
Battlestar Galactica, the new series. After the basestar leaves with Roslin and Baltar on it, we first see how the fleet reacts, focusing on Lee Adama. The next episode takes place at the exact same time, but from the perspective of the people on the Basestar. Notably, we see the aftermath of the Battle of the Resurrection Hub before we see the actual battle.
The daytime soap The Young and The Restless does this with a few scenes from the end of the previous episode played at the start of the next to keep the viewer current without disrupting flow.
Technically different shows, but one episode of Buffy the Vampire Slayer showed Spike's victory over his first Slayer and Angel congratulating him. Then the episode of Angel shown immediately afterward revealed that Angel had his soul at the time, and the tone of his congratulation took on a very different interpretation.
Eastenders once depicted a two-hander featuring Peggy and Pat at Pat's house which ended with their fight being interrupted by a ringing doorbell. The following episode was another two-hander featuring Pat's husband Roy and Peggy's fiance Frank (who was also Pat's ex husband). The plots of the two episodes came together at the end when Frank and Roy returned to Pat's house and and rang the doorbell just as Peggy and Pat's fight from the previous episode was in full flow.
The Leverage episodes "The Girls' Night Out Job" and "The Boys' Night Out Job" happen simultaneously, the former following Sophie, Parker, and Tara as they investigate a thief who's trying to steal secrets from the Venezuelan government and sell them to the highest bidder, the latter following Nathan, Hardison, and Eliot as they try to help out a former mark turned good who's inadvertently gotten roped into what appears to be a drug smuggling plot (again).

Video Games

The first chapter of Gears of War 3 is split into two segments that happen concurrently and focus around defeating a Lambent Leviathan. The first half is played by Marcus, Dom, Anya, and Jace as they defend the Raven's Nest and use it to push the Leviathan under a bridge. The second half is played by Cole, Baird, Clayton Carmine, and Sam as they locate and deploy a sufficient explosive at the Leviathan from atop the bridge to, as Cole puts it "blow its brains out its ass."
The Swamp Camp section in Dreamfall is seen through the eyes of all three protagonists, who arrive at different times but all come together by the time the Azadi troopers storm the camp. The visual clue and the synchronization point is the flare signal seen by every protagonist as the approach the pier.

Web Comics

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Western Animation

South Park had the three-party Meteor Shower Trilogy taking place on the same night: the first episode had Cartman babysat by Stan's sister Shelly while his mom was at a party; the second part showed Stan with his parents at that party, which the government thought was a Heaven's Gate-style cult meeting; and the third had Kyle and Kenny at a camp for Jewish kids, where a villain tried to summon an Eldritch Abomination Biblical Bad Guy.
Fairly Oddparents had an episode concentrating on Timmy's friends investigating him which was set during an early episode, "A Wish Too Far", in which Timmy had been trying to become popular. There were overlapping scenes, and partially overheard conversation, from the earlier episode.
"Heat" and "Snow" on Hey Arnold!.
- Actually, no, though "Snow" seems to have begun shortly after "Heat" ended.
"The Wrong Address" and "The Wrong Customer" on Chowder
Phineas and Ferb has done at least two pairs of these sorts of episodes, "Unfair Science Fair/Unfair Science Fair Redux" and "Bubble Boys/Isabella and the Temple of Sap"

Web Original

The "Emma and Lilith" find-the-difference games come in paired sets, one for each girl's perspective of the same story. The scenes in Lilith's games are highly detailed paintings with a dark-ish color palette, while Emma's resemble childrens' book drawings and are colored in bright pastels.