A window manager in a Unix context is software that controls the placement and appearance of windows under the X Window System.
A desktop environment is a much larger system, offering a complete graphical user interface (GUI) to the computer. On systems running the X Window System a desktop environment typically consists of a window manager, a file manager, a set of themes (colour schemes, aka "skins"), and programs and libraries for managing the desktop. All of these individual modules can be exchanged and individually configured to achieve a unique combination, but most desktop environments provide a default configuration that requires minimal user input. They also include the concept of "session management", which means that when you log out the nature, size and position of open windows is stored, and when you next log in the environment will attempt to open the same windows in the same places.
Changing Window manager/Desktop environment
At the login window, somewhere on the screen but most likely at the bottom left will be Session. Clicking on this will bring up a list of the window managers and desktop environments which have already been installed on that particular machine, as well as other possibilities such as "Last" (whatever was last selected), "Default", and "Failsafe_Terminal" (see below). Simply select the one you want, and type in your id and password.
If you wish to use a window manager or desktop environment which is not on the list then you will have to login using some other window manager and install it yourself. This can be done using the instructions at Software installation under Unix. (Note that installing something like GNOME or KDE will bring with it hundreds of other dependent RPMs!). Once it is installed, log out of your current session and the new manager/environment should now appear on the list of Sessions you can select.
The Failsafe Terminal is an environment with a single window which does not start the X server and does not source any of the usual "dot" configuration files (such as .profile) which you might have in your home directory. It is intended as a way in when everything else is going wrong - for example if you have made a faulty modification to one of your configuration files which results in login failure.