What is the actual story behind the M-4 Carbine?

CAR 15 XM16 XM177 M16 M4, all variations of the same rifle

That looks like the CAR-15 Commando, which also had a shorter stock (XM177/GAU-5 series).

Shown the standard size M16 and the shorter version often referred to as the Car 15, or otherwise more officially as the XM177. In our unit the 366th Security Police Squadron locatated at Da Nang, Viet Nam when I was stationed there in 1968-69 Most of us carried the standard Colt M16 but the smaller carbine version was used by our K9 troops. they needed one hand for the dogs leash and the shorter weapon was easier to handle for them so they could handle both the weapon and their K9 partner. Notice also the strap on the Carbine version on top so they could put that over their shoulder and not have to put the weapon down if the needed both hands for the dog. Our unit, the 366th SPS had 45 dogs, all German Shepard's. that kept it so it could be carried at the handlers waist level and in a position ready to be used. They worked mostly around the perimeter post both the USAF section and sides of the base and also around the post from the USMC on the other side of the Base. The Marine's 1st MP BN, which had 3 companies had no dogs, the USAF dog handlers covered their post areas and our own as well. The Colt M16 was a replacement for the Armalite AR15 and the Car 15 reference kind of stuck for the XM177 even though Colt made both versions that are shown in the picture here. As pointed out by SP5 Keane, CW3 Storm and LTC Broom on each of their post here some of the same information and history of variants of this weapon, I guess between the four of us everyone should get most of the story right here.