You may be a little confused about exactly what GNU/Linux is. What's the Linux kernel, vs. the GNU utilities, vs. the X Window System? Here's a little ASCII art diagram to show you how it all relates (apologies, it's not very attractive).
Window Manager ----- Gnome Programs/Libraries (in development)
| | ----------/ \
| | / ---------\
| X Clients Programs/Applications ---- Shared Libraries
| | \ | /
\ | ---------------\ | /-----------
X Server -------------- Linux Kernel
| / |
| /--------------- |
Video Card -------- Other Computer Hardware (Memory, disk, etc.)
Note that the X Server and X Clients are applications, but they are applications which interact in special ways with the video hardware and other applications.
The window manager is a special X Client, and thus also an application. All the X programs use the Shared Libraries, but no line appears in the diagram.
When the Gnome (GNU Network Object Model Environment) project is completed, it will help to unify the X environment with a special set of programs and libraries, interacting with the window manager and other X Clients.
The GNU utilities are small programs that do simple tasks: mv, cp, tar for example.