Correction "GFL M38 9mm" is "Model 1938" for use in MAB38A submachine Gun. To distinguish cartridge from the standard Italian service cartridge, 9mm Corto, M34 (1934) which is a .380 Auto/9x17 Corto.
Nothing to do with "military", although the major users were the Italian Military ( and Africa Colonial Police).
Cartridge identical to 9mm Parabellum, in dimensions, but load and bullet different, as required by a heavy , long barreled Machine Carbine ( "Moschetto Automatico Beretta".).
Gun itself better in range and hitting power than any other of the WW II 9mm subguns, except maybe the Finnish SUOMI K31.
regards,
Doc AV
AV Ballistics