Yes, there are three breeds that are "true" pit bulls: the Staffordshire bull terrier (in England), the American Staffordshire terrier (an AKC breed), and the American pit bull terrier (not AKC, but recognized by the United Kennel Club)

And yes, the term "pit bull" is used as slang to mean other dogs of similar shape.

As for "double-hung" -- it doesn't have any anatomical meaning. The trainer probably just meant that such dogs have strong jaws for their size (pit bulls are bred for strength). They don't have any special "locking" mechanism or other major anatomical difference from other dogs.