The vertical grip is a military issue plastic grip which attaches to the bottom of the Picatinny rail at the bottom of both the M4 Carbine RAS both the M5 Rifle Rail for the Mk18 Mod 0, M4A1 Block 1 and the M16A4 military rifles.
This is made by Prudent American Technologies (PAT) (formerly known as P&S Products), who produces accessories for military weapons. This item is identical to the Knights Armament KAC vertical grip, but is marked with the PAT (or P&S) CAGE code. PAT, along with Colt and Knights and other manufacturers, all build to DOD spec for M4A1 weapons systems. PAT also makes the M4 quad RAS and the Colt M4 buttstock.
The military grade vertical grip is made of two parts. The bottom part unscrews to loosen the grip on the bottom Picatinny rail, and tightens back up to lock in place, while not marking the RAS rail. The VFG was originally placed on the bottom of the M4 Carbine RAS made by KAC and also by PAT-P&S Products for the M4 Block 1 and also for the Mk18 Mod 0, which shared the same quad rail. Later, when the M16A4 was developed, a similar RAS quad rail was made by both manufacturers in rifle length to snap into place between the rifle delta ring and the end plate at the front sight post.
Note: One pic depicts a KAC vertical grip for illustration. These are 100% the same, but branded PAT (or P&S Products).