Not sure about CS (although I'm almost positive it's just an upgrade of Photoshop 7.0). I believe it's like an expansion pack to the existing program. Unfortunately, I haven't upgraded to it yet. It's a tad on the pricey side (almost 200 bucks just for an upgrade

).
but as for the difference between elements and and the full version...
Elements is a darn good program for the price (which is a lot less than Photoshop). It has almost all the tools, brushes, and filters of the full photoshop.
However, Photoshop (full version) has several key tools that elements does not (healing brush, art history brush). It also has layer masking...which is so darn cool
Photoshop full also has much more customizable layer styles and effects. Then of course there is the biggest difference--Photoshop comes with Image Ready. It's an indispensible program that allows you to EASILY create animated gifs and to compress the size of your files in all formats. You can do this in elements, but it's a heck of a lot more difficult.
I'm sure there is a lot more little nuiances that I'm skipping...but that's the gist.