Ok, I'll give this a shot. Keep in mind I don't breed or show cats so I'm going by the CFA, TICA and breed club websites.
The American Bobtail is recognized by CFA and TICA. It derives from a natural mutation in domestic cats. DNA tests have found no wild (ie Bobcat) markers. Feet have the normal number of toes front and back.
Pixie Bob is recognized by TICA. Another natural mutation in domestic cats. Again DNA tests have found no wild markers. Pixie Bobs can have polydactyl feet.
Outcrosses are not allowed in either breed. So no breeding the two together.
Reading the two standards there are differences in head shape, feet, colors allowed, etc. So these are two separate breeds.
Hope this answers some of your questions. I sure learned something new.
By the way The Messybeast Cat Resource Archive has a page on bobtail, tailless and kinky tail mutations in domestic cats if you want to read more.