It does. In an NPN transistor, it collects electrons, and in a PNP, it collects holes. ;-)
Oh! I see your confusion! The emitter current is the sum of the base and collector currents, but you seem to have had the impression that "collector" implied that the collector current would be the sum of the base and emitter currents? That's OK, and not a hard mistake to make first time out. Don't worry - it gets lots easier with a little practice. :-) I guess you could say that the collector collects whatever didn't get diverted to the base. Historically, it's called the base, because it was literally the base - like those galena crystals with the cat- whisker - and the emitter and collector were two cat-whiskers. (or maybe safety pins. ;-) )
Cheers! Rich