There is only one version of Little Palm Pet, and the pets are designed to be somewhat generic. They're not really exactly like a dog or a cat, in appearance or behavior, but you do have some degree of control over the appearance of your pet at the beginning of the game. While you are in the Adoption Center (at the beginning of the game, or if you decide to give up the pet you have and adopt a new one) you have the ability to keep rejecting pets until you find one with an appearance that you like.

It would be nice if the game offered pets that were clearly puppies or kitties, but it's still fun to play.