So... the question isn't what is an aspie, but why do we use the word aspie to describe us? Or... if I understand the question, why use any word at all to differentiate us from the rest of the population. You said something like "Why do we need a differentiating name? We "just" people."
I'll attempt an answer. Yes, they are people. I don't know that they are "just" people, but people they certainly are. However, they have a social condition, which you probably know a few things about since you're here. People with AS may hardly be debilitated at all; some might be moderately debilitated; and some may be very debilitated. The same goes with people who are quadriplegic. Some may be hardly debilitated (in theory), some may be moderately debilitated, and some may be very debilitated. Does it not make sense for them to have a special name (quadriplegic) for them?
We have that name (Aspergian, aspie, sufferer of AS, etc.) because it identifies an abnormality or problem they, as a group, have. they're people, but they're different from the rest, and that name is an indicator of how they are different.