Let me start out with the following:
Mac OS, Mac OS X and Mac OS X Servers are three
entirely different OSes. So, Mac OS isn't Mac OS X,
and Mac OS X isn't Mac OS X Server. Here we go.
 
Mac OS

Mac OS
Mac OS, once simply named "System", is the standard operating
system for the Macintosh, which you're probably running right now. The
current version is 9.1 and runs on any PowerMac. screenshot | website
 
 
Mac OS X

Mac OS X
Mac OS X, codenamed Cyan/Siam and to be released 24 March 2001, will be Apple's most revolutionary operating system yet. The X doesn't only stand for 10, but also for the fact it's unix-based. Mac OS X will have pre-emptive multitasking (every program will get as much processing power as the rest, not just the foreground), protected memory (meaning programs will run independently from eachother so when one crashes, the rest will happily go on), and will run Mac OS applications, Cocoa applications and Carbon applications. Also, a BSD is included, which offers the ability to run any compilable unix commandline program. The regular Mac OS can still be run in the Classic environment, which will run applications that were written for the classic Mac OS seamlessly.

Mac OS X will have a completely new interface compared to that of the original Mac OS.
Shadows, 3D-ish effects and glowing buttons make the user feel as if the Mac has become a living 3D artwork.

The system requirements for Mac OS X aren't certain yet, though officially they are "targeted" for G3 and G4 Macs. Rumor has it that Apple might still try and get Mac OS X to run on some of the pre-G3 PowerMacs as well, but there's no guarantee. screenshot | website

Click here for a more detailed explanation of Mac OS X and its core.
 
Mac OS X Server


Mac OS X Server will be released shortly after Mac OS X. Mac OS X Server is what you could call the Server edition of Mac OS X: An OS not meant to be used continuously by a user working on it, but rather as an OS dedicated to perform the tasks that a server is meant to do, such as running a webserver, AppleShare server or WebObjects server. Mac OS X Server will in any case run commandline programs and Cocoa applications. Wether Carbon applications will be run or wether Classic.app will be included I don't know, although I have a feeling that Mac OS X Server will basically be Mac OS X, only stripped down and built up to a robust Server OS.

screenshots | website
 
 So what's the difference ?

Mac OS X and the regular Mac OS are not the same.
Mac OS X and Mac OS X Server have their own version numbers
and are OSes way superior to the regular Mac OS. While Mac OS X
and Mac OS X Server are Apple's main focus, the regular Mac OS
will continue to develop for those without X experience/needs, or
without the required hardware to run any sort of Mac OS X.

Mac OS X and Mac OS X Server are not the same either.
Mac OS X Server is already here. It's a server OS.
Mac OS X is the consumer version, coming somewhere 2000,
and will be the full blown version, without the server parts.
Once, Mac OS X was referred to as Rhapsody 2.0, where
Mac OS X Server would be Rhapsody 1.0. After Rhapsody DR2,
they changed to Mac OS X Server and Mac OS X. Mac OS X (Consumer)
will be much more like the Mac OS than Mac OS X Server is, since
it's for the consumer, not for server machines. Mac OS X will have
a beautiful new yet familiar interface, with the strength of UNIX underneath.
In other words, Mac OS 10.
 
 Miscellaneous

Codenames.
Mac OS 7.0.0: Blue
Mac OS 7.1.0: Cube-E, Tripoli
Mac OS 7.5.0: Capone <------- Capone terrorizes Chicago, codename for Windows 95 :)
Mac OS 7.5.3: Buster <------- Gil Amelio's high school nickname
Mac OS 7.5.5: Son of Buster
Mac OS 7.6.0: Harmony
Mac OS 7.6.1: Ides of Buster
Mac OS 8.0.0: Tempo
Mac OS 8.1.0: Bride of Buster
Mac OS 8.5.0: Allegro
Mac OS 8.5.1: The Ric Ford Release
Mac OS 8.6.0: Veronica
Mac OS 9.0.0: Sonata
Mac OS 9.0.1: Minuet

Mac OS X/10.0 Server: Rhapsody
Mac OS X/10.0: Cyan / Siam

Mac OS X Sub-codenames:
Public Beta: Kodiak
Final Release: Cheetah
(Speed optimized)

"Copland" was once the codename for what Apple had planned to eventually
become Mac OS 8. Mac OS 8 as it exists now was originally supposed to be
named 7.7 (Tempo). Apple's plans have since changed in such a manner that
the codename Copland vanished, and Mac OS 8.5 now more or less is what
Copland was planned to become.

Timeline.
Apple's original plans for OS releases. Mac OS X Server (Rhapsody) was

delayed till April, and Mac OS X has been delayed till March 24, 2001.

Corrections/addendums can be sent to sixkiller@ukonline.co.uk