The AKC recognizes the American Staffordshire Terrier and SBT. The UKC recognizes the American Pit Bull Terrier and the SBT. Take note of the phrase "dog displaying a majority of physical traits of any one or more of the above breeds..." This definition will encompass mixes. Also, since majority legally means "51%, this could (if literally enforced) apply to many, many breeds (including American Bulldogs, Jack Russell Terriers (Parson Russell Terrier), Boxers, Bull Terriers, and many, many other breeds. If you read the standards, they are actually fairly general for all breeds. IN fact, one court said an "American Bulldog" was a "PIT BULL" because it had similar physical characteristics. In fact, most short-haired dogs of bull and/or terrier origin have similar characteristics when reduced to paper. Dogs of all breeds are ALL the same species. They interbreed (hence, same species), and genetically are fairly indistinguishable. Hence, they tend to have very similar physical characteristics, especially when grouped into things like "terriers" and "Hounds." Amstaffs, incidentally, are in the terrier group.

Here is an example of how standards can be very similar for different AKC breeds. Take the "head" as specified in the AKC standard for the Amstaff and the Labrador Retriever (and the head is arguably the most distinctive feature of the Amstaff, so if the head has so many similarities between two unrelated breeds, anyone can see how problematic this "majority of physical traits" definition of Pit Bull is):

AST Head
Medium length, deep through, broad skull, very pronounced cheek muscles, distinct stop; and ears are set high. Ears - Cropped or uncropped, the latter preferred. Uncropped ears should be short and held rose or half prick. Full drop to be penalized. Eyes - Dark and round, low down in skull and set far apart. No pink eyelids. Muzzle - Medium length, rounded on upper side to fall away abruptly below eyes. Jaws well defined. Underjaw to be strong and have biting power. Lips close and even, no looseness. Upper teeth to meet tightly outside lower teeth in front. Nose definitely black.


LAB HEAD:
The skull should be wide; well developed but without exaggeration...  The head should be clean-cut and free from fleshy cheeks... The jaws are powerful and free from snippiness-- the muzzle neither long and narrow nor short and stubby. Nose-- The nose should be wide and the nostrils well-developed. The nose should be black .. Eyes--Kind, friendly eyes imparting good temperament, intelligence and alertness are a hallmark of the breed. They should be of medium size, set well apart, and neither protruding nor deep set.

You  can do this with lots of breeds. Note the overlap (i.e., some of the language may differ, but the physical traits end up being the same --- lab: wide skull ast: broad skull what is the difference between wide and broad? Nothing.

lab head clean cut and free from fleshy cheeks ast head: lips close and even, no looseness (so, clean cut and free from fleshy cheeks)

lab: muzzle neither long and narrow nor short and stubby ast: muzzle medium length.... (that's a shorter way of describing the lab's muzzle)

lab: eyes set well apart and medium size
ast: eyes set far apart.

lab jaws: powerful and free from snippiness
ast jaws: well defined, underjaw to be strong (same thing, different words)

Now, if you compare the standards, you can find 51% similarities between
them... so under the law as literally applied, all labs could easily meet
the definition of Pit Bulls (you see why lab mixes are often labelled "Pit
mixes?")