For your second question, a window manager is the specific system that controls the placement of windows on an X11 desktop.
On a X11 based system, X11 is the windowing system (interacting with the video card) and a window manager is a system sitting on top of that laying out the windows and interacting with the user and other programmes. It is a separate programme on top of the X11 system, and communicates with X11, and X11 is the programme that communicates with the graphics card.
On Wayland, instead of 2 separate systems there can be 1 combined windowing systen that is both the window manager but also directly communicates with the hardware in a standardised way using the Wayland protocols. This is called a Wayland compositor.
Meanwhile a desktop environment is the whole desktop - that includes a window manager or compositor but also lots of other tools and software that together make a full desktop experience.
An example is KDE - KDE is a full desktop environment. It uses its own x11 window manger called kwin (and also able to be a wayland compositor), but it also uses a whole range of other tools alongside that to give you panels, widgets, desktop icons, a clock, menus, settings etc collectively forming Plasma desktop. And then on top of Plasma there is a whole range of bespoke programmes that form the full deskop experience - like Dolphin (file manager), Kate (text editor) and so on. All that software is designed to work seamlessly with the KDE family of tools and systems. The window manager, the desktop tools and the other programmes together form the whole desktop environment. But other desktop environments software will also work - for example Gnome based software can also run with KDE without issue and vice versa.
Gnome has its own window manager/compositor, and it’s own widgets and tools to make a desktop, and it’s own bespoke software to make a whole desktop environment.
And there are many others.
So in summary:
Window Manager - the specific system that controls the placment and look of the individual windows talking to X11 which then talks to the hardware
Wayland Compositor - the system that controls the placement and look of windows, using wayland protocols to speak to the hardware
Desktop Environment - the whole desktop including the Window manager but also lots of other programmes and tools that form the basic desktop (such as a panel, menus, desktop icons) and the whole environment (other software like a file manager, text editor, calculator etc). KDE and Gnome are examples of popular desktop environments
For your second question, a window manager is the specific system that controls the placement of windows on an X11 desktop.
On a X11 based system, X11 is the windowing system (interacting with the video card) and a window manager is a system sitting on top of that laying out the windows and interacting with the user and other programmes. It is a separate programme on top of the X11 system, and communicates with X11, and X11 is the programme that communicates with the graphics card.
On Wayland, instead of 2 separate systems there can be 1 combined windowing systen that is both the window manager but also directly communicates with the hardware in a standardised way using the Wayland protocols. This is called a Wayland compositor.
Meanwhile a desktop environment is the whole desktop - that includes a window manager or compositor but also lots of other tools and software that together make a full desktop experience.
An example is KDE - KDE is a full desktop environment. It uses its own x11 window manger called kwin (and also able to be a wayland compositor), but it also uses a whole range of other tools alongside that to give you panels, widgets, desktop icons, a clock, menus, settings etc collectively forming Plasma desktop. And then on top of Plasma there is a whole range of bespoke programmes that form the full deskop experience - like Dolphin (file manager), Kate (text editor) and so on. All that software is designed to work seamlessly with the KDE family of tools and systems. The window manager, the desktop tools and the other programmes together form the whole desktop environment. But other desktop environments software will also work - for example Gnome based software can also run with KDE without issue and vice versa.
Gnome has its own window manager/compositor, and it’s own widgets and tools to make a desktop, and it’s own bespoke software to make a whole desktop environment.
And there are many others.
So in summary:
Window Manager - the specific system that controls the placment and look of the individual windows talking to X11 which then talks to the hardware
Wayland Compositor - the system that controls the placement and look of windows, using wayland protocols to speak to the hardware
Desktop Environment - the whole desktop including the Window manager but also lots of other programmes and tools that form the basic desktop (such as a panel, menus, desktop icons) and the whole environment (other software like a file manager, text editor, calculator etc). KDE and Gnome are examples of popular desktop environments