Are you talking riot/trench guns or training shotguns?
The military has used a wide array of shotguns over the years, particularly during WW I and II. In addition to the commonly seen Winchester Model 1897 and Model 12 trench and riot guns there were also many longer barreled models used for aerial gunnery practice so it's not beyond the realm of possibilty to find ordinance stamps on what otherwise might appear to be hunting guns.
The vast majority of what you'll see will be pump guns of various types but at least some semi's were used. I can think of the Remington Model 11 off the top of my head. I just saw a riot version of that at a show this month and they also used longer barrel models for the above mentioned gunnery practice. From what I've read the Model 11 riotguns were used stateside by factory gaurds etc, and not for combat use.
Another one to keep an eye out for is the Remington Model 10. These were WW I issue guns in both riot and trench configuration. They were the rarest of WW I issue shotguns apparently. I say this with some chagrin as I moved one only a few months ago without fully knowing what I had
. I could find zilch on it in books, from collectors or on the web. Condition was fair at best and it needed fixed (failure to cock when cycled). Concensus was that it must have been a cutdown either used originally as a gunnery model or possibly cutdown for gaurd use. I swapped it for an AK and thought I got the better end of that deal.
Maybe not as it now appears. At this past gunshow my brother picked up a newly printed book on the weapons of WW I. It has a fair section on the Model 10. The first place we've seen anything on it and they give purchase numbers and variation details. After reading that we're pretty confident that what we had was in fact a correct WW I riot version of the Model 10. Oops
. I still can't say I came out of it bad as I had zero invested in it (it was given to my family by a widow who just wanted it out of the house) and the condition was pretty bad, but I wish we'd have known what we had first.
Ah well, live and learn. Point being there are quite a few variations and models out there both in the realm of riot and trench gun, and gaurd and training shotguns. As you get later towards the Vietnam era you'll also see Savage pump shotguns, Rem 870's, Ithaca 37's, Winchesters 1200's (I'm pretty sure they were pre-1300 guns) and Mossberg 590's both 20" guns with full tube and bayonet lugs and 20" tubes with the shorter mag tube and no bayonet lug.