As far as I understand it:
- X11 is how you draw primitive things;
- A (compositing) window manager is something that uses X11 to provide the tools for drawing more complex things, and position them in layers on screen;
- A desktop environment is something that uses a window manager to provide the bare essentials of a GUI-based operating system, like a control panel, calculator and solitaire apps, task bar, etc.
If my understanding is correct - what is Cinnamon? Its wiki article (and the tag here on SU) describe it as a "desktop environment", but I can't find what window manager Linux Mint uses by default in its wiki article, and the Tara release notes mention improving the "window manager" in the Cinnamon 3.8 section.