yeah, it's a lot to take in.
XP and Vista are "work station" OS's. These run on every day computers.
Windows Server series run on Servers - duh - and they are built with similar technology.
No, as a typical user, you will never see Windows Server anything.
Servers are great big huge computers which host things like web pages (called a web server) or applications or email or files.
A Server OS has the added tools necessary to allow these functions. For instance, there are certain things that need to happen for a server to "host" a web page, it has to allow incoming and outgoing connections and blah blah blah - same if you are working an email server (such as MS Exchange).
You install Windows Server just like you would install XP; in fact many regular machines today are plenty powerful enough to run Server 2003 (and sometimes they do, though it's not recommended).
I do good with pictures. So here; have pictures:
Each of those boxes is a server. Each one could potentially be running Windows Server 200x. Or each one could be storing files available to an entire company.
Anyone know of any good diagrams to illustrate a corporate network???
EDIT:
Here's a good example;
http://www.pc-utilities.net/sde-layout.gif
Each of the machines on the bottom is something that you or I use on a daily basis. The big box that they all link to is a server. In this example, this server is used to manage the antivirus software. However, that antivirus manager is just a program. That program is run by Windows Server 200x. Windows Server provides the tools needed for the antivirus manager to work.