In rescue, every dog we get is identified by its breed. If we don’t know what breed it is, we guess. The most popular breed guesses are Shepherd, Lab, and Pit Bull Terrier mixes. But we never just say “mixed breed” without including at least one identified breed. That’s because if we want to identify them on PetFinder.com or other adoption websites, they usually require a breed category to place them into.
Cats are different. The majority of cats are identified simply as “Domestic Short Hair” or “Domestic Long Hair”, which I believe is another way of saying they don’t have any specific identifiable breed. And other than my one experience with some Pixie Bob/Desert Lynx cats, which turned out to look just like Domestic Short Hair cats, I have never fostered any type of purebred cats.