The best measure of furriness is if human parts have been replaced. Catgirls have additional ears and likely a tail but all the normal human parts. If you replace the limbs with paws, then it immediately becomes furry.

This also solves the question of whether catgirls have two sets of ears. The answer is yes, they're just sometimes covered by hair. Unless the artist explicitly shows nothing on the side of the head, in which case it is actually mildly furry and not a true catgirl.