The first gun is the US Mark 1 Remington 870.
This is an ordinary 870P Police gun with a 20" barrel and the standard factory extension, which the military designated as the Mark 1.
These were 2 3/4" guns since the 3" wasn't invented yet.
In any event, the military used only 2 3/4" shells anyway.
The factory extension barrel clamp wasn't strong enough to support actual use of the bayonet, so a special long barrel and extension clamp/shroud was made up to fit over both the barrel and the factory clamp.
This had a factory front rifle sight base attached to the top, and a bayonet lug and sling swivel on the bottom.
The original factory front sight base was removed from the barrel so the clamp would slide over the barrel.
On many guns, the front sight blade, and the rear sight windage and elevation assemblies were removed, leaving the rear sight base on the barrel, and the front base on the clamp.
On the gun pictured, the standard stock has been removed and replaced with some sort of sliding stock, and there is a light or laser mounted under the barrel.
Most guns have the standard factory wood stock and no light/laser.
The original guns were standard factory Police satin-black blued, although many if not most have since been parkerized.
The Mark 1 barrel clamp/shroud turns up from time to time on Ebay, but price is SKY HIGH for what are usually badly worn, often pitted units.
No commercial copy has ever been made.
The second gun is a factory-stock Remington 870P Police Tactical model with the 14" barrel.
Here's their web site on it:
www.remingtonle.com/shotguns/870tactical.htmThe gun has a synthetic full stock, a 14" barrel and the standard 4 shot plus 1 in the chamber capacity.
The guns are parkerized and have a bead sight.
These under 18" barreled guns can be bought if you are willing to go through the NFA procedures AND your State allows their possession.