What you should know, before trying to understand the rest of this document.
The OOUI interface is currently a part of the Berlin project, in particular, it is one of the kits. Thus, the Berlin terminology is inherited.
Berlin is a new user interface system. It is designed to be highly modular and standards-compliant. Its current implementation is developed as a direct replacement for the X windowing system, but nothing in general restricts it to Unix. Nobody tried it yet, but it an implementation for MacOS should be possible. For more info, see Berlin's FAQ.
There are two definitions for server within Berlin:
Berlin uses the X-way of thinking here: The server side is responsible for the I/O and the application run as client.