A Linux workstation is running an X server as well as all
the applications (word processor, web browser). It operates
the same way a normal desktop computer does.
A Linux computer running only the X server and relying
completly on other Linux computers to run the applications, is
called an X terminal. Because its task is simplified
a lot, a much less capable machine handles that easily.
A Linux computer runing applications for X terminals is called
an application server.
Note that these are only conventions. Nothing prevent
an application server from being another type of server
(file server, web server, ...) or from running an X server
to display on its own screen.