Linux Basics/Graphical interfaces
X Window System does the job for graphical display under Linux. We also call X Window System as X or X11. Its GUI is very plain, but it's a graphical server, so it gives home to many desktop environments and window managers.
Login can be on graphical interface:XDM(X Desktop Management), GDM, LightDM, SDDM etc.
Every operating system has its own graphical package manager, like Synaptic under Debian-based systems, Fedora has dnfdragora, Arch has Pamac or Octopi, etc.
Important Desktop Environments and their logos:
There is also Cinnamon and MATE which can be mentioned, they're both Gnome-derivatives. (Arch wiki has all the Desktop Enviroments explained) You can choose which you want to install under Linux, customization has no limits.
Composite Window Managers e.g.: Compiz, Compton, Xfwm, Marco, KWin.
The Window Manager does the job for window operations (minimize, maximize, move etc), compositor does the effects, like at minimizing the window slowly vanishes etc.
You can change the Window Manager and Desktop Environment under operation (but when you install them, you may have to quit from the current DE and re-login to see the changes)