It's not overly technical, just has more nuance :
A Window Manager is a type of compositor or X client (depending on if it's based on Wayland or Xorg respectively) that manages the placement and appearance of windows on the screen.
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It is responsible for the appearance and behavior of windows, determining the border, title bar, size, and ability to resize windows, and often providing other functionality such as reserved areas for sticking dock-apps or the ability to tab windows.
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It can be part of a Desktop Environment(DE) or be used standalone.
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Often times when WMs are referenced it's in reference to standalone WMs which are often keyboard centric and come in various different forms. For example tabbed, tiling, dynamic, stacking, dynamic tiling, etc.
Some popular Xorg based WM in Linux include i3, BSPWM, DWM, Awesome, Fluxbox, Openbox, WMii, Xmonad, etc.
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Some popular Wayland based WM including Sway, Hyprland, River, DWL, NeWM, etc.
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Then there's WMs built-in to Desktop Environments like Kwin(KDE Plasma) and Mutter(Gnome).
If you're interested there's an Arch Wiki with even more info.