I'm wondering that is there any differences between Gnome-Global menu and Appmenu-indicator? Or are they just only one? Which one is still being developed?
Global menu is old and I don't think it is being actively developed anymore.
Application Menu is under very active development by the Ubuntu community and Canonical employees.
Application Menu supports way more apps than the old global menu.
appmenu-indicator is designed to be a desktop agnostic way to provide for a "global menu" from GNOME, GTK, and QT applications.
gnome-global-menu is GNOME/GTK specific.
That is just the surface. Programatically, there are several underlying fundamental differences.
The loose description of each might seem the same but I would focus on appmenu-indicator in Ubuntu for the best integration of all "Ubuntu provided" software.