What Is A Mutt
A stray dog is a dog with two different breeds (eg: Beagle = stray dog) whose past is not necessarily known (parents), most people consider a stray dog to be a dog of unknown origin. Any cross breed, even this design dog (whatever it is, a way to get people to pay the maximum price ...) is a mute. But stray dogs are the best dogs :) I have a stray dog and he is the sweetest. And I love all the design dogs, I just don't think they should be called breeders and all breeds of dogs should be named Haviden and Goldndoles.
Stray dogs are a mixed breed. If there is more than one breed, the dog is wild. End of history.
You will have people who claim to have branded puppies. This is not a problem.
Purebred dogs are just one breed and one breed of dog. They are usually recognized by big dog clubs like AKC, UKC, Caian KC, etc. If not, they are more likely to be identified by a rare breed association.