Yes, 9mm goes by many names. Like 9mm, 9mm Luger, 9mm NATO, 9mm parabellum and 9×19. All exactly the same round, only difference is what the manufacturer decided to call it. Just make sure it's not 9×21 or 9×23 because that's a different cartridge. Hope this helps.

Short Answer....Absolutely yes!!!!

Stanley, yes Sir. 9mm (by itself) 9mm Luger, 9mm NATO and 9x19 Parabellum are the same. 9mm to stay away from in a 9mm handgun are 9x18 (Makarov), 9x17 (.380) etc. Cheers and shoot safely!