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Well, they would be a different species within the animal classification I’d assume (regarding the big cat).

But say a poodle and a cocker spaniel breed, that new breed within the dog species doesn’t make them a wolf, right?

All of the cat species, from the house cat to the jaguar to the tiger, in the New World and the Old World, were once the same animal (whether you accept Creation of "kinds" or evolution), yet there are huge differences among them now. If you put a group of chihuahuas in a different environment (islands are classic) where, perhaps, the primary easily accessible food was grain, how long would it take before the descendants of the chihuahuas were indistinguishable from rats? (Assuming you can tell the difference now :D)