If I understand that A creates a process on B which is, in fact displayed on A: The display window is provided by the window server on 'A,' hence A is called the server. The process on 'B' that created the window is called the client process. Admittedly this sounds back-assward, but it is the view of the windowing system.
in reply to Terminal across network
If, however, A creates a window on itself, and in the window it connects to B in order to run a process on B, then, from the window management point of view, A is both the server and client. From the application point of view, assuming that A's window connects to a server on B, A is the application client.
It is important to separate the windowing environment from the application environment IF THE APPLICATION IS NOT A WINDOW BASED APPLICATION. Once the distinction is made as to which is the server and which the client, then the appropriate client and server code can be written.