fuzzy hairy white caterpillar critter

About a week or so ago a friend sent me a photo of a critter to see if I could identify it.  I couldn't

This morning I walked out and noticed these lying on the patio!  EWWWWWWKKKK!

It's the same darn critter!

 Looking up I saw these in my sour orange tree; they are moving, crawling, so I am assuming (yes, I know what they say) that they are some kind of caterpillar.

I have searched and searched the internet and my books and can not figure out what they are.

If they are just butterflies or moths then I'll let them have a few leaves and be on their way, but if they are going to damage my tree I want them gone!

Can any of you help me to identify them?