Desktop environment is like traditional windows desktop, everything included. It has stuff like notification daemons, advanced settings, toolbars, task manager and so on.

Window manager let's you manage windows but often doesn't have it's own toolbar, notification demon, task manager and other things. People who run window managers are picking their own toolbar software, their own notification daemon and so on. They want a much more customizable personal experience, often heavily themed as well. Usually a window manager is also faster than a desktop environment since it does less things.

Compositor is what gives drop shadows, transparency and other visual effects. Its often built into desktop environments but is often missing from window managers, but not always. When it's missing, people install one of their own. There are a few popular choices.

Examples of desktop environments: Gnome, KDE Example of window managers: Sway, Hyprland, i3, xfce, awesome wm