Compassion is when you feel sorry for the situation, pity is when you feel sorry for the person.
What I mean is that when you pity them, it kind of overwhelms your view of the person and you treat them as if all they are is someone to be pitied. The guy in a wheelchair isn't a quirky funny guy with a coffee addiction and a sort-of girlfriend, just a pitiful person who can't walk. Compassion you still see the person as more than just a victim of misfortune.
Pity for autism is acting as if meltdowns and inability to do things makes up the entirety of autism and not seeing the good. Compassion for autism is feeling sad because the kid's having a meltdown and doesn't have the verbal skills to tell you what he needs, but also seeing his sheer glee at watching a fan and valuing that.
That's my opinion, anyway. It's not about what you do or don't do, it's about how you see the person.