When an X11 client starts, it looks for information about an X11 server that is capable of handling the graphical user interface. This is usually done by looking at the environment variable DISPLAY. This environment variable, if defined, specifies the default X server. It usually has the format of localhost:0.0, which means the network address is localhost, and the X Window display 0 and screen 0. This implies that an X11 server can handle multiple screens in a display, and multiple displays on a computer.
Just about all GUI programs in Linux are X11 clients, as Linux does not specify a GUI, at all. This implies that an X11 client also does not have to be a Linux program. For example, a Windows program that understand how to use X11 as a protocol can be an X11 client. More interestingly, a Windows client can run on a Windows machine, but its server can be on a Linux machine!