My understanding is that introversion may be partly about ability to socialize, but primarily reflects lack of desire to socialize ( and especially lack of desire to socialize in larger versus smaller groups). It’s also my understanding that with AS, there is at least sometimes a component involving inability to socialize, for example, many of those with AS have a hard time reading facial expressions (and this inability comes not merely from lack of practice, but is more innate).
I have also met a number of people with AS who are extroverts, that is, they have a desire to socialize, although they may have some difficulties in execution. I don’t have any breakdown on the numbers, but it seems to me that if introversion is more about lack of desire to socialize and AS is more about inability to socialize, they don’t necessarily need to be correlated, although they may very well be.
One definition I've seen is that extroverts get energy from being with people, while introverts need to be alone to recharge.
Followup to: Do you have High-Functioning Asperger's Syndrome?
LW reader Madbadger uses the metaphor of a GPU and a CPU in a desktop system to think about people with Asperger's Syndrome: general intelligence is like a CPU, being universal but only mediocre at any particular task, whereas the "social coprocessor" brainware in a Neurotypical brain is like a GPU: highly specialized but great at what it does. Neurotypical people are like computers with measly Pentium IV processors, but expensive Radeon HD 4890 GPUs. A High-functioning AS person is an Intel Core i7 Extreme Edition - with on-board graphics!
This analogy also covers the spectrum view of social/empathic abilities, you can think about having a weaker social coprocessor than average if you have some of the tendencies of AS but not others. You can even think of your score on the AQ Test as being like the Tom's Hardware Rating of your Coprocessor. (Lower numbers are better!).
If you lack that powerful social coprocessor, what can you do? Well, you'll have to run your social interactions "in software", i.e. explicitly reason through the complex human social game that most people play without ever really understanding. There are several tricks that a High-functioning AS person can use in this situation: