From my reading of apples os x server page, the server will be the client plus apple share ip, mac manager, and all the other goodies bundled with the server previously. My understanding is they're the same os but the server has extras to facilitate gui file sharing and server type activities.
One other included thing is a utility to run clients, IE: you have an old mac that can access shared drives
That sounds about right for the current versions--I read this as a slightly different question, which I'll answer as well (that way, whichever Zax meant, he gets his answer).
Mac OS X Server, up to the end of last year, was a shipping, independent OS, one generation back from the current OS X, which is what used to be referred to as OS X client. It's somewhat similar, but apparently has rather a dull interface... Apple stopped selling it relatively recently, and proposes to replace it with the package described above.
From what I've heard, OSXS was originally Apple's solution to the problem of having a great Web Applications platform (WebObjects, acquired with Steve, Avie and that company of theirs) and no OS that it could run on--I guess they pushed it out the door without consumer-level stuff like the GUI changes as a stopgap measure (and at $499, relatively few non-server customers were going to snap it up, protected memory or not).
I started this from memory, then looked up a little of the more detailed stuff (good thing, too--I was dead wrong on a couple points). I found a Macworld article from about when it shipped, which has some of the above and a little more (http://macworld.zdnet.com/1999/06/news/whatsin.html)--there's probably still a fair amount of info out there about it, since a bunch of people still use it.