It's going to vary wildly based on a lot of different things.
An Imperial world that regularly sees Craftworld Eldar visitations (or invasion) would probably, if faced with a Harlequin or Drukhari, recognize that this isn't the 'normal' Eldar they're used to.
Most Inquisitors probably know the difference, if not a great deal about each kind (for non-Xenos inquisitors). Most servants of the Inquisition (particularly Ordo Xenos retinues) probably have a good idea, too.
Some Space Marines may, some may not. It seems unlikely that ravaging chapters like the Space Sharks or the Marines Malevolent would know, or even care. Others, like the Salamanders, have been fighting Dark Eldar since before the Heresy, and so even their line troopers probably know the difference.
Particularly, chapters who have lost recruits to the DE (Space Wolves, White Scars) might be likely to educate even their newest members on the dangers of Aeldari (which could conceivably include their different sub-factions).