Yes. To add onto this, the bulldogs/staffs/whatever you’d call em were brought over from the UK as fighting dogs and bred in the USA as American Staffordshire Terriers. The USA wanted a dog they could call their own to boost country morale, so they started creating the distinct breed of American Pit Bull Terrier. The AKC wanted to distance itself from dog-fighting, so they would not accept the APBT to be registered. People had been breeding the American Staffordshire to look a certain way, while others were breeding the APBT specifically for dog-fighting, the AKC allowed Amstaff, and that is where the “show-type” of dog comes in. Amstaffs are essentially the show-bred version of APBT, in a whole seperate breed. The UKC allows APBT and AmStaff to be dual-registered, meaning you can register your AST with the AKC as an AST, and you can also register it as an APBT with the UKC.
(Or something like that, based on my knowledge)
I believe the dual registry works this way: you can register your AKC-registered AST with the UKC as an APBT, but you cannot register a UKC-registered APBT with the AKC as an AST. this was my understanding a few years ago so the rules may be different now.