(like Ubuntu vs Ubuntu Server, server is just additional software.)
Let's say that the desktop and the server editions are DIFFERENT software. Ubuntu is a desktop OS with a full graphical user interface and Ubuntu Server is a full server platform WITHOUT ANY graphical user interface. Repeat: no GUI at all, leave your mouse at home, you won't be needing it. Instead, Ubuntu Server comes with options to be installed as a cloud server, a LAMP stack or for other typical server-only tasks like file and print or database or directory services.
But you are right that both Ubuntu versions use the same repositories and that with sufficient work one can eventually do what the other does or be configured to become the other edition; they are just pre-packaged for completely different uses.
While on the other hand, the OS X client before Lion could never become a full OS X server, at least not when you wanted to replicate or use Apple's proprietary server software and tools on the desktop version of the OS.
When I first read about, I still thought that they would be releasing another version of OS X server. But then I visited Apple's website and their wording didn't leave much room for interpretation: Yes, whatever server features Apple wants to save are now becoming a part of the standard package of OS X Lion. There won't be a separate server edition anymore.
And it makes sense. They buried their server business, so they don't need to develop, market, ship and support a separate server OS anymore.