The X Windows manager is concerned with how (application-)windows look like and where they are created.
A window manager draws the borders (frames) around windows. It also controls the placement and size of windows.
Usually, a window manager is started as last program from ~/.xinitrc.
Implementations
Some window manager need a desktop-environment, others, such as WindowMaker, sawfish, fvwm etc don't.
Other implementations: Openbox, metacity (practically unusable without GNOME), twm (which has been the standard window manager for X since version X11R4) etc …