That cartridge has a lot of names. Probably due to the rather limited civilian production, commercial companies seem to have often just used their ".45 COLT" headstamp bunter, resulting in both .45 Colt and the shorter .45 having the same marking. (And this led to the designation ".45 Long Colt" vs .45 Short Colt?)
The shorter round has been called .45 S&W, .45 Schofield, .45 Gov't, .45 Army, .45 Short Colt, and .45 Colt Gov't.) Headstamps on commercial ammo were ".45 COLT", .45 S&W", and ".45 C GOV'T"
The Army called it none of those; to them it was just the .45 Revolver, Ball, since it was the only .45 revolver cartridge being issued. The Benet primed rounds had no headstamp; later CF rounds had only the Frankford Arsenal and date stamp. Commercial ammo was made in limited quantities for the few S&W Schofields sold on the commercial market by S&W and those sold as surplus later, but the Army issued ONLY ammo made by Frankford.
So now that clears up everything? Sure.
Jim