Most of the concepts here are the same for wayland. The only difference is, Wayland handles compositing, whereas in x11 compositing is a pluggable component.
A Wayland compositor is responsible for quite a bit more than an X11 window manager. Compositing, as you mentioned, but also display modesetting, input handling, clipboard management, and so on. Although, of course, one can use a library like wlroots or libweston to handle most of that stuff if you just want to focus on the desktop experience.