Most of the models I've seen have been gate-based; there are certainly a wide variety of physical implementations for the same logical gates. You're right that the D-Wave system (if it's real) is different, but are there really that many other non-gate models?
Not exactly. Quantum computers are a kind of analog computers based on quantum mechanics and there are several different models for doing quantum computation ---only one of them is based on gates. Annealers such as D-Wave aren't based on quantum gates.
They instead slowly anneal the system to its ground state (while avoiding states corresponding to a local minima in energy), and the usefulness of this lies in the fact that calculation of ground state of a system is often an extremely difficult problem, and that you can map your NP problem onto calculation of the ground state in certain cases.