Not That Kind of Mage

Basically, this is when one type or tradition of mage is mistaken for another, or someone mistakenly assumes that the mage would fit an incorrect pop culture version of a wizard.

See also Not That Kind of Doctor, Magic A Is Magic A. (This is a case of Magic A is not Magic B.) Un-Equal Rites can be a result.

Anime/Manga

 * Koizumi Itsuki in Suzumiya Haruhi is sort of like this,despite supposedly being an ESP-er. He cannot read minds,or move things with his mind unless he is in a closed space. Even if he's in a closed space,he still can't read minds.
 * However he(and the other memebers of his organization) can feel Haruhi's emotional state.
 * A variant appears in an early arc of Mahou Sensei Negima, where Negi is dying due to slow petrification and Evangeline can only fret helplessly as undeath and mastery of healing spells do not mix well.
 * Or just that she'd never had any reason to learn healing magic before, as neither she nor any of her usual companions would benefit from it.
 * Early on, Negi has to inform Asuna that her pop-culture expectations of magic (stuff like trees that grow money, etc.) isn't how magic actually works. There's also a section of the series dealing with differences between western mages and eastern mages.

Literature

 * Harry Dresden gets this a lot, even though his ad in the Yellow Pages states specifically what he will or won't do. Some of these are actual magical limitations, while others he follows according to his personal code or the laws of the White Council.
 * And he doesn't do parties.
 * One Mercedes Lackey story (starring Tarma and Kethry) features an unusual variant where the one suffering misconceptions is the Mage; the antagonist has a very weak mage Talent, which means she can only handle a limited amount of raw power and is innately incapable of working many powerful magics. She just isn't very good at magic either. Yet she is thoroughly deluded that power and skill are irrelevant, and all one actually needs to become a full Adept is knowledge. She becomes obsessed with the idea that her teachers are keeping "the secret" of full Adepthood from her, and goes thoroughly crazy.
 * In the Dragonlance setting there are four types of magic, Wizardry(sometimes called High Sorcery, and draws from the world's three moons), Clerical Magic(Magic granted by the gods), Primal/Wild Sorcery(which draws from the planet Krynn itself) and Mysticism(which comes from all living things). The former two are called "Focused" magic, while the latter two are called "Ambient" magic. The first two are called Focused because they are focused through either the Moons or through a god, where as Ambient magic comes from Krynn itself and the living things on it. Mistaking a Wizard for a Sorcerer might annoy them a little bit. Mystics and Clerics tend to get along better.
 * In The Belgariad, sorcerers have a powerful form of Inherent Gift, while magicians summon and "control" demons. Calling a sorcerer a magician is seen as very insulting. (Ironically, Belgarath is both, though he normally relies on his sorcery and is smart enough to only summon a demon when a). he absolutely needs to and b). it's not very powerful. He still only does it once across ten books).
 * He's also not above disguising himself as a magician and using sorcerous illusions to make it look like he's summoned a demon. Again, though, once in ten books.
 * Beyond that, there are Witches (well, a witch). She even gets the differences confused at one point, asking Belgarath to perform a spell that she can't, then offering him the use of any spell components he needs (sorcery is a completely mental thing). There also exist wizards (Only one of whom is ever named, but an entire city of them exists at Kell), but the reader never sees any wizardry, and thus has no idea what they do. One of the sorcerers remarks on peoples inability to keep the various varieties of magic straight, noting that most people take everything they've ever heard about any of them, and lump it all together with the assumption that any person who is capable of any of that fantastic stuff is capable of doing all of it.
 * Possibly averted in that Belgarath himself later in the series explains that all of these different magics come from the same source and talent and that the differences are, ultimately, cultural. Specifically Sorcerers were tought by Gods and use pure Will to make things happen, Magicians use the Will to summon and (fail to) control demons, Witches use the Will to ask natural Spirits to intercede on their behalf (the aforementioned spell components being offerings to said spirits). And Wizards also do... something... with the Will.
 * This happens periodically in The World of Ethshar because magic is very complex indeed:
 * Wizards tap the fundamental chaos of the universe for powerful, and astoundingly unpredictable, results. (One was trying to create a sword sharpening spell and ended up creating a pillar of eternal flame the size of a mountain.)
 * Sorcery taps the fundamental order of the universe in order to make powerful magical devices. Sorcerers once went to war with Wizards so one assume they are fairly powerful, but they lost so they don't do all that much currently.
 * Warlockry allows one to rearrange the matter with their own mind; by communing with an Eldrich Horror (probably) that eventually eats the magic user (most likely).
 * At one point one villain discovers that there is another warlock power source that seems not to have any Eldrich Horror so a warlock who stays near this one and far from the original one gets safe and unlimited power.
 * Witchcraft does much the same thing as Warlockry, but using the witch's own power which makes it more limited.
 * Demonology is the summoning and control of demons. Really handy for killing people, not so much good for cleaning the house.
 * Theurgy is summoning and attempting to talk gods into doing what you want them to do. Less handy then one might suppose as the gods tend to be difficult to work with at best.
 * Telemain from the Enchanted Forest Chronicles frequently gets mistaken for a wizard (who only knows one type of magic) when he is infact a magician (who studies many kinds of magic) albeit one who is particularly interested in finding out how wizard magic works and interacts with other types of magic. Also, nobody likes wizards in that series, and with good reason.

Role Playing Games

 * The Unknown Armies supplement "Post Modern Magick" notes that adepts have had problems with working in organised crime because the mobsters were uninformed about their powers and gave them orders like "make Vinnie's car invisible", when the adept talents ran more to, as an example, finding out secrets instead.
 * In most Dungeons & Dragons settings, most commoners are not expected to know the difference between a Wizard and a Sorcerer. This will probably get even more confusing to them when you include non-core full casters, like the Beguiler (a stealthy illusionist expert) or a Warmage (whose only spells that aren't straight up blasting are the "Light" cantrip, doing Exactly What It Says on the Tin, and Elemental summoning spells, which call up destructive embodiments of the classical elements).
 * And let's not forget mages who specialize in different schools of magic. A sorcerer who specializes in divination magic probably knows nothing about transmutation.
 * Pathfinder takes it up a notch. It has the traditional D&D core casters, but then adds in the Witch (a debuff/mezzer with light damage and healing), the Alchemist, the Summoner (a medium-duty caster with a pet monster), the Inquisitor (a leader-type hybrid of rogue/cleric), the Magus (a hybrid wizard/fighter), and the Oracle (a sorcerer-like divine caster) to the Core classes. Most of the old 3.X line is also compatible. It can overwhelm new players but also allow old players very different takes on the generic "caster" variants.
 * Psionics in early editions (up to AD&D) were an entirely bolted-on system which Gary Gygax, the creator, reputedly felt pressured to include. Their rules did not jive with any other part of the Vancian Magic system and could snap balance like a twig in most settings. Later editions had clumsily integrated psionic powers and classes. The powers in early editions were wildly different from anything in D&D's default western fantasy tone. By 4th edition, psychic powers were integrated, but they also ceased to "feel" different than all the other magic abilities out there.
 * Mages in Mage: The Ascension can all pull off exactly the same feats, though most have specialties working in their area. They differentiate on how they believe they work magic. For example, almost every mage will decide to make a general purpose "heal self." A Son of Ether will create a magical injection of "nanobots" who repair their torn flesh, while a Hermetic might call upon alchemical principles and European mysticism, an Akashic Brother might harness their qi, and a Cultist of Ecstasy might take sexual healing literally. If you try to work magic against the core beliefs you established at character creation, it won't work. For example Etherite can't steal and drink the Hermetic's alchemical slop and expect anything good to come out of it. Even if all the magi are creating the same effect, they can't use each others' schtick (paradigm, in game).

Video Games

 * Uncommon but still present in World of Warcraft. Mages, how many times have you been asked for a soulstone or summon? Warlocks, how many times have you been asked for a portal or food and water? Come on, we all know it's happened at least once.
 * Due to some classes having to chose to specialize in only one of multiple potential roles this would happen to many non mage classes. A druid may be invited to a party to heal when he has allocated all his talents to becoming a giant bear and mauling people, or to do damage when he had specialized in being a slow moving healing tree that couldn't even cast offensive magic in his preferred form. The Wrath of the Lich King expansion lowered the occurrence of this by allowing classes to specify which roles they could perform when looking for a group, many players of Shadow priests or Enhancement (melee) shaman still expect them to heal.

Webcomics

 * In the D&D-inspired webcomic Order of the Stick, wizard Vaarsuvius is deeply insulted when another wizard refers to hir as a warlock.
 * V's rage may have had less to do with his/her recent evil actions than lampshading that the warlock is a Tier-Induced Scrappy. V's a prototypical arrogant wizard who disdains all other arcane casters of any sort, and the warlock was frequently considered a terrible design by the fandom.
 * In the webcomic The Dragon Doctors, Sarin the wizard is a master of transforming people but is unable to transform clothing, resulting in quite a few wardrobe malfunctions.

Web Original

 * Comes up in Unskippable with a mock conversation complaining about the weather and that the mage can't change it, and pointing out that Steve could do it. The retort is that Steve's a weather mage, so of course he could.