Puss Moth, or Asp Moth

Karen, I believe only the caterpillars sting.

The adults are also fuzzy- do their hairs sting too, or just the caterpillar?

They are also called Southern Flannel Moths and yes, the caterpillars do indeed sting! Here is another resource from online about this interesting creature:
http://bugguide.net/node/view/4476

OOOH!!! Definitely DO NOT TOUCH! This is the Puss (as in a kitty cat) Moth, or Asp Moth. iT IS VERY VENOMOUS! (I'm not kidding.) Those attractive hairs pack a very painful wallop! I strongly suggest you read the article in wikipedia I posted the link to.