Amstaffs are Pitbulls & both are related to the Staffordshire Bull Terrier.
A pedigree is a recording of ancestors. The dogs don't even necessarily have to be of the same breed.
Many "old timers" kept meticulous records of their working dog breedings in ledgers, exercise books or written on the shed wall. I cleaned that up)
A "pure breed" doesn't necessarily have to be registered or even have papers if it meets the criterior of breeding to type every time.
Registered, recognised pure breeds are a different story.
