All of that's correct, as far as I know. Just note that a Wayland compositor must implement some core Wayland protocols and it can also implement its own proto

All of that's correct, as far as I know. Just note that a Wayland compositor must implement some core Wayland protocols and it can also implement its own protocol extensions (for example, it can implement a screen-sharing extension, and efforts are being made to 'standardize' these extensions).