There is a small terminology issue here: a "server" is a program that offers services to remote "client" programs. The clients make requests and the server responds to them. A client program will make a request like "allocate me a chunk of the screen and put these here bits in it", or "let me know about any of these events that happen". The server manages the screen and notifies the clients about things they're interested in.
I agree, it actually does make total sense - but that doesn't mean I won't get confused :).
My only prior exposure to "GUIs over the network" were web applications, where the roles are essentially reversed. That is, the part responsible for accepting user input and rendering the UI is the client (the browser), and the part that performs the application logic is the server.
I naively assumed that X would work the same way, but it wasn't too hard to unlearn that misconception.
There is a small terminology issue here: a "server" is a program that offers services to remote "client" programs. The clients make requests and the server responds to them. A client program will make a request like "allocate me a chunk of the screen and put these here bits in it", or "let me know about any of these events that happen". The server manages the screen and notifies the clients about things they're interested in.
IT MAKES PERFECT SENSE, DAMMIT!