1 Except for Boston Terriers, they are generally included in kennel clubs' Terrier Group. 2  Some breeders have bred modern Bull type terrier breeds, such as the Bull Terrier, American Pit Bull Terrier and Staffordshire Bull Terrier, into suitable family dogs and show terriers. Included among these breeds are the English Toy Terrier and the Yorkshire Terrier. 2  While small, they retain true terrier character and are not submissive  lap dogs 3  . Bull type Terriers: The Bull and Terrier types were originally combinations of bulldogs and terriers as general mixed breed bull-baiting and pit dogs.