Debian has two menu systems
The official one is the Freedesktop Desktop Menu Specification, which was adopted as the primary menu in Gnome, KDE, LXDE and others. It is famous for the *.desktop files in /usr/share/applications.
The optional, so called Debian menu system provides a centralized list of all installed user applications (for which the packager provided a menu entry). It is a documented in the DebianPolicy. Those menu entries are available in most window manager / Desktop environment in Debian (KDE, GNOME, ?GNUStep, ?Enlightenment and ?Windowmaker, making every application available in every environment). Each application drop a menu entry in /usr/share/menu/ and menu manager register to menu by droping an entry in /etc/menu-methods/.
In 2014 the Debian technical committee was asked to choose between these two menu systems (741573) and in september 2015 it decided that the preferred menu system is the Freedesktop one.