GNOME is part of the GNU Project and developed by The GNOME Project which is composed of both volunteers and paid contributors, the largest corporate contributor being Red Hat. It is an international project that aims to develop software frameworks for the development of software, to program end-user applications based on these frameworks, and to coordinate efforts for internationalization and localization and accessibility of that software.
GNOME 3 is the default desktop environment on many major Linux distributions including Fedora, Debian, Ubuntu, SUSE Linux Enterprise (exclusively), Red Hat Enterprise Linux, CentOS, Oracle Linux, SteamOS, Tails, Kali Linux and Endless OS, as well as Solaris, a major Unix operating system; and provided as an official edition by Manjaro; also the continued fork of the last GNOME 2 release that goes under the name MATE is default on many Linux distros that targets low usage of system resources.
GNOME Flashback is an official version of GNOME 3. It provides a similar user experience like the GNOME 2.x and provids a traditional desktop.
GNOME Shell is the default graphical shell of the GNOME desktop environment. The application menu displays the name of the application in focus and provides access to functions such as accessing the application's preferences, closing the application, or creating a new application window.
Beginning with GNOME 3.8, GNOME provides a suite of officially supported GNOME Shell extensions that provide Applications menu and "Places menu" on the top bar, and a panel with windows list at the bottom of the screen that lets quickly minimize and restore open windows, a "Show Desktop" button in the bottom left and virtual desktops in the bottom right corner.