GNOME is a desktop environment (it handles the desktop icons and panels).
Metacity is one of GNOME's window managers (it keeps windows organized).
GTK+ is GNOME's widget toolkit (it draws the buttons and checkboxes).
X11 is the window system (the thing that draws the windows on the screen).
Xorg is an open-source implementation of X11 (usually synonymous with X11).
Compiz is a window manager and desktop compositor (a desktop compositor is a program that renders special effects, such as a desktop cube, on your screen).
You can run Compiz in GNOME, KDE, and Unity at least. Just get the CCSM package by entering this into the terminal:
$ sudo apt-get install ccsm
(Don't enter the dollar sign and the space after it; these just mean that you are not logged in as root.) In CCSM (Compiz Config Settings Manager), turn on and configure whatever desktop effects you want. Be careful! You may lose the titlebars in GNOME and UNITY. If that happens, press Ctrl-Alt-F1 and then type in:
Look under the PID column and note the number on the xorg entry. Then enter:
$ sudo kill pid
The login screen should appear immediately. Log in again and avoid making the mistake your did last time. Sorry for the long discourse.