I once read that cats and dogs were commensals (ate at our table); both had jobs to do (cats hunting rodents, dogs warning, hunting, herding, guarding, antiwolf-wolf, etc.). Animals kept and tamed for meat, milk, wool/hair, hides, bearing burdens are domesticated. Animals kept for fur are mostly wild animals kept in cages. The one attempt to breed more docile foxes also gave them neotenous traits like floppy ears and spotted coats. That breeding program, 40 years old or more, is still struggling along despite a desperate lack of funds in the former U.S.S.R.
Oddly no one seems to have taken credit for domesticating the pig, unless it’s the farmers of New Guinea. At least one author hypothesized that they just moved in with us as equals.
I understand that a ferret is a domesticated polecat(?).
But when we consider the odd friendships that animals sometimes form with each other, it’s not surprising that almost everything has been kept as a pet/friend/household member.