In Spain, at least, people will often refer to a pet dog or cat as a “perrito” or “gatita,” that is, the dimunitive, while “perro” usually refers to a working dog or dogs in general, and “gato” (or gata) refers to feral cats or cats in general.
Nobody really uses mascota much in conversation (it’s more to describe something such as a law affecting pets, a product for pets, etc.), and I’m sure it’s a fairly new term.
I see; where my wife’s family is from, they’re all working dogs (Galicia); I don’t think they ever even had cats on their farms.