The "General" is the H&R Model 65, front sight has the 'ears' that became prevalent with the M1 and follow-on US military arms, a 1/4 minute Redfield aperture rear sight, the ones that the Corps purchased are marked "Property USMC" and are Parkerized. They're also known as the Reising Model 65. The operation is a bit odd, the action is cycled by inserting your finger into the forearm and pushing the op-rod to the rear. They use a 10 round magazine, and have an odd bolt hold open device on the right side of the receiver.
Mine does not have the stamped metal trigger guard, nor the winged front sight, having instead a ramped bead on a post.
The Reising .45 ACP sub-machine gun's operation is quite similar, but was never especially liked, and not nearly as reliable in the jungles as the Thompson or M3 "Grease Gun".
The Ordnance Corps also purchased a LOT of H&R Model 12 bolt action rifles that are very close to the Model 52 Winchester, except that they're single shot only, and the 52's can be either single shot or repeaters. The Model 12's are also marked "US Property".
I also have a US Property marked Mossberg Model 44 that came from the CMP a couple years ago, and it is a shooter, as well, just doesn't have a very nice trigger, but once you get past that, if it doesn't hit what you're aiming at, you did something wrong.
I've also got a US Model 1922, that is a clip-fed rimfire adapted Model 1903 Springfield, and a more beautiful 'Big People' .22 you'd be hard pressed to find!
The US Military has used a LOT of commercial arms pressed into service as trainers.
Several years ago, 'they' remodeled the main chow hall at Hill AFB in Utah, where I was working till I retired. When they pulled down the interior walls, almost every square inch of the original wall surfaces was covered with original War II "propaganda" posters, ala "Rosie the Riveter" and "Loose Lips Sink Ships" type stuff. Those all came down and as far as I know, went to the Hill AFB Museum adjacent to Roy, Utah.
The history of the US Military training arms is immense, long, and colorful, and a guy can dump a BUNCH of time, effort, and money into collecting them!