Not all .mil contract shotguns are heavy barrel. The A1 is, and some versions of the 500 are. Most of the Army's shotguns are not heavy wall.
There are something like 7-10 NSNs that Mossberg has provided to the .mil and not all of them specify A1 equipment.
Most of the government contract shotguns are 500s with many not having the heavy barrel, metal safety, or metal trigger guard.