Wayland is a communication protocol that specifies the communication between a display server and its clients, as well as a C library implementation of that protocol. A display server using the Wayland protocol is called a Wayland compositor, because it additionally performs the task of a compositing window manager.
Weston running on postmarketOS
Compositing window manager
A compositing manager, or compositor, is software that provides applications with an off-screen buffer for each window. The compositing manager composites the window buffers into an image representing the screen and writes the result into the display memory. A compositing window manager is a window manager that is also a compositing manager.
Flip switching in Compiz