This is one of those situations where the story and fluff of the game world is dropped a little bit in the name of game mechanic simplicity.
Eladrin don't really know the spell 'Misty Step'. Instead, they have a special eladrin ability to teleport called 'Fey Step' which mechanically matches the same ability spellcasters can do that they have called 'Misty Step'. So while the game uses the spell 'Misty Step' as a shorthand to describe what 'Fey Step' does... the two are not one and the same. And for the sake of the story of the world... calling the feature 'Fey Step' and describing how it occurs and is used should really be done differently by the eladrin player than how the wizard player would describe what happens when they Misty Step.
It's the same thing that occurs with Warlocks. They have all these invocations to their patrons whose mechanics match the spells that clerics and wizards have... but those invocations really aren't spells. Invocations and spells should really be considered, run, and described completely differently. Otherwise, all the flavor of being a warlock just goes away and you end up being nothing but just another magic-user.
Now perhaps this is just a personal bugaboo on my part... but if you're a warlock with Eldritch Sight... but when you use that invocation you say 'I cast Detect Magic'... you fundimentally are destroying the fluff and story of your own class. Because you aren't casting Detect Magic, you're using your Eldritch Sight. Yeah, the rules the DM has to use to adjudicate that are exactly the same... but the story of what your character is doing is different. If you chose to play the fluff-heavy Warlock class... then to my mind, you should and would play up that fluff that makes you different than any other regular magic-user, even if mechanically the rules are run the same way.
But again... maybe that's just my own hang-up.