Well... I make things that one might call "art," and therefore, I wouldn't feel like a jerk for calling myself an "artist." It does, however, irk me when people say that I'm an "Anime artist," because drawing in an Anime style is not my intention. crying I suppose the influence is there, but everybody keeps overlooking the fact that I'm not Japanese. I consider this a prerequisite for being an Anime artist, I guess.
I think trying to find a term other than "artist" would muddy the situation too much. I could call myself an "Art student," but isn't everybody who is interested in or makes art a student? If you're doin' it right, you're learning all the time!
The best art advice I have ever heard (but haven't been smart enough to follow) was this: Carry a small sketchbook with you everywhere, and put it to use on a regular basis.
I do love me some artin'.