Introversion is a personality trait. Introverts can socialize, but we prefer one-on-one environments or small groups to crowds, we prefer spending more time with intimates to meeting new people, and in general, we see social life as a cost rather than a benefit.

Asperger's, from what I've read of the subject, is a cognitive issue; Aspies don't read social cues that neurotypicals (including introverted neurotypicals) pick up on without even thinking about it, and therefore have trouble socializing even when they want to.

It's like the difference between people who don't read a lot of books because they prefer to spend their free time watching TV, and people who don't read a lot of books because they're dyslexic.