What is the difference between a windowing system (for example X11, Wayland) and a window manager (Awesome, Compiz, OpenBox)?
What you refer to as a windowing system is more commonly referred to as a display server.
The differences between display servers are well documented. But, the difference between a display server and a window manager is in the job that they perform. A display server handles displaying graphical applications and relaying input and output from graphical applications to the rest of the system and vice versa.
On the other hand, a window manager's job is to manage how (or more often, where) the display server displays its client windows.
As a result, almost no one uses a display server without using a window manager of some kind (though it is possible). You can more simply think of this relationship like so: The display server displays everything graphpical, and the window manager organizes the client windows for display by the display server.