The APBT and the AmStaff are roughly the same thing. Think of it as the AmStaff being the show type and the APBT being the working type. A Staffordshie Bull Terrier, or Staffy, is a different breed from the other two. Saffies are smaller and stockier, while the AmStaffs/APBTs are slightly larger and leanier. It can get be very confusing to understand the differences between all the bully breeds. Esspecialy since everyone seems to have a different name for the exact same thing, or people will lie and say they're dog is one of the other breeds and not a "Pit Bull". Here's some pictures that ma help illustrate the differences.
APBT
AmStaff
Staffy
APBT

AmStaff

Staffy
