GNOME and KDE aim to be fully-functional, integrated desktop environments. They consist of a number of different programs that all look and act similarly, and can be customized in a common way. GNOME can be found at http://www.gnome.org/, and KDE can be found at http://www.kde.org/.
No, they are not. GNOME and KDE work with a number of different window managers, and encompass much more than the simple manipulation of windows. However, each one of them recommends a window manager that "works best." For GNOME, the recommended window manager is Enlightenment, and for KDE it is the included KWM. Other window managers, such as Window Maker, integrate well with both GNOME and KDE.
As of this writing, KDE seems to be further ahead in terms of end-user ease of use and installation, while GNOME has numerous technical merits. Try both out and find which appeals to you more.