Although Pitbull is actually known as Pitbull, this is a generic name. Dogs called Pit Bulls consist of four hybrid and pure breeds: American Pitbull Terrier, American Staffordshire Terrier, American Bulldog and Staffordshire Bull Terrier.
As you can see here, there is no phrase of pitbull in the expression of most breeds. In other words, the breed of most dogs that we usually see on the street or in shelters and say "Oh look, Pitbull!" Is not actually a Pit Bull, it is probably one of the above breeds.