X-Server is the gui desktop you are running.
No the X-server in NOT the gui desktop, that would be the Window Manager ie. KDE, Gnome, Fluxbox. The X-server allows the WM to work. They are two separate things but work together, you can run X-server session without the use of a WM but you can't run a WM without a X-server session running.
Fallow reply #3 to stop the X-server from running.