The pets do need the training to understand that the sounds, when the button says them, mean communication to the human. It’s actually a pretty sophisticated intellectual jump, and not all pets necessarily get it.

Typically one starts with “outside” as a non-food common request (for indoor peta). So an owner starts by saying “outside” and associating just that word with going outside (not the full “you wanna go out?”). Once the pet gets past the conceptual hurdle is the button means the thing, after that it’s much easier to add new words.