Basically, all of the above are Ubuntu, but the install CD's contain a different collection of packages based on what you want to do.
Ubuntu -- gnome desktop environment
Kubuntu -- KDE desktop environment
Xubuntu -- XFCE desktop environment
Edubuntu -- contains educational type packages (standalone client version)
Edubuntu is really made for thin client setup, i.e. setup one central server and all the clients are just used as remote keyboards, monitors, and mice. All the programs are run off of the central server.
As for the rest:
Live CD -- runs entirely from CD and won't install to the hard disk unless you ask it to
Desktop -- installs common desktop (email client, web browser, etc) packages
Alternate CD -- gives you the most control over what to install, you choose what to install
Server -- installs common server packages (apache, email server, etc)
Get Ubuntu from Ubuntu's website