I'd like to think that there are distinct animals, if only so we can bypass stuff like the prospect of people eating Tauros meat. And arguably Pokemon all originated from outer space or Ultra Space, so it's unlikely, but possible.
In my head, Pokemon managed to breed with native Earth life and gradually displaced them. The majority of farm animals are purely Earth species, although Miltank do provide most of the supply of milk. People having a domesticated cat or dog, while much rarer than, say, a Growlithe or Purrloin, isn't unheard of.
