How many Imperials know the difference between the different types of Eldar?

I know it probably doesn't make a difference to the average forge-menial, but would, say, an Astartes captain or an Ordo Xenos inquisitor know the difference between the various flavors of Eldar? Does this fact change after the events of the Gathering Storm?

An Ordo Xenos Inquisitor would certainly know the difference between all the subcultures of Aeldari, it's their job after all, as would a death watch space marine, probably.
As for the regular Space Marine Captain he may not now, nor care based on the bigotry of his chapter.
Maybe a Space Marine Librarian.

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).