Complex sentence: Pit bull is the common name for a type of dog, not a recognised breed in its own right, formal breeds mistakenly referred to as such include the American Pit Bull Terrier, American Staffordshire Terrier, and Staffordshire Bull Terrier.
Split into simpler sentences: Pit bull is the common name for a type of dog. Formal breeds considered as such include the American Pit Bull Terrier, American Staffordshire Terrier, and Staffordshire Bull Terrier.