According to the Wikipedia Article for Window Managers, here's what they stand for:
A window manager is system software that controls the placement and appearance of windows within a windowing system in a graphical user interface. Most window managers are designed to help provide a desktop environment. They work in conjunction with the underlying graphical system that provides required functionality—support for graphics hardware, pointing devices, and a keyboard, and are often written and created using a widget toolkit.
In simpler terms, a window manager is a program that deals with placing, removing, and just managing the placement of window.
What Desktop Environments does Andronix offer?
Andronix supports almost all the major DE(s) that the current Linux community has. These include Awesome, i3 and Openbox.
Desktop Environment List
Ubuntu Awesome i3 Openbox
Debian Awesome i3 Openbox
Kali Awesome i3 Openbox
Manjaro Awesome i3 Openbox
Fedora Awesome i3 Openbox
Void Awesome i3 Openbox
Arch Awesome i3 Openbox
Which WM should I choose?
You can pick whichever WM you like or you are familiar with. However, for the most part, we recommend going forward with a Desktop Environment if you're new to Andronix. This is because operating WM without an actual keyboard can be unpleasant. That being said, if you're ready to explore, pick up Awesome.