You are running in fact Ubuntu.
There are few differences, most importantly, whenever you need to start a program, the liveCD needs to run it from the CD, which is slower. Also, you cannot save anything permanently (unless you specifically attach ie. mount your hard disk).
Finally, an installed system will be better tuned to your hardware, faster, and more up-to-date (packages on the LiveCD may be obsolete).
One caveat are proprietary drivers, notably Nvidia drivers. Nvidia drivers (which have 3D support) cannot be installed automatically by the Ubuntu installer, so if you have Nvidia, after the installation instead of the eye-candy of a 3D desktop you will have a much less eye-catching 2D desktop. However, Ubuntu will then tell you that you should install the Nvidia drivers from the Nvidia site, and you will be able to do so with a single mouse click, after which you will have your nice desktop back.
Otherwise it's pretty much the same stuff.