Patton had a Bull Terrier, not quite a "pit".
I believe "Bull terriers" "American Staffordshire Terriers", "English Staffordshire Terriers" and a few others are referred to as "pit bulls" I think "pit bull" is a catch-all term used to describe any type of fighting terrier breed formerly used in dogfights conducted in pits and isn't really the name of a specific breed.
Of course, I have been known to be wrong, but I do know quite a bit about dog breeds.