I always thought that XWindows uses the term 'client' and 'server' correctly, while the average joe simply uses the words too loosely: they want to say that the client is "my machine right here", and the server is "that machine over there".
But, in reality, it is the display server process that offers display services to client programs that use them.
But, in reality, it is the display server process that offers display services to client programs that use them.