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.
Best Answer
Cinnamon is a desktop environment, as its wikipedia page and archwiki page both state.
Cinnamon uses its own window manager called muffin, installing the cinnamon package also installs the muffin WM package on Debian.
Cinnamon also has "a bundle of programs running on top of a computer operating system, which share a common graphical user interface (GUI)" as Wikipedia's Desktop environment says as a basic definition. Its programs are X-Apps, but like all programs they're generally voluntary if you want to remove & use others instead.
Additionally, the archwiki page also states: