The "CAR-15" has a long history, with numerous variations. I am going to give you the Readers Digest Large Print Version.
When the US sent special forces advisors to Vietnam, some of them were equipped with the XM177E1, equipped with a 10" barrel and 3.5" sound/flash suppressor, aka the CAR-15.
[b]WARNING: WAR STORY AHEAD!![/b]
When I flew Cobra helicopters in Vietnam way back towards the middle of the last century of the last millenium, we Cobra drivers lusted after the XM177E2, which we called the CAR-15, because it fit into the cockpit of a Cobra without breaking it down. I myself never got my hands on one and was reduced to carrying an M16A1 with the rear takedown pin open so I could squeeze it between the armor plate and the canopy inside the cockpit. The XM177E2 had an 11.5" barrel with a 4.5" sound/flash suppressor.
(We also lusted after illegal to possess Swedish K's, folding stock AK's and M3's.)
Sometime after the Vietnam conflict, the XM177E2 came under criticism from the Warsaw Pact Nations for it's "illegal" sound/flash suppressor. This largely concerned the status of prisoners of war who were captured with such weapons and/or wearing camouflage when captured.
Troops with silenced weapons and/or wearing camouflage could be immediatly shot on sight as spies, according to the Warsaw Pact's interpretation of the treaties.
There was an incident when US soldiers, driving US military vehicles, conducting legal inspections in East Germany, were shot by Russian troops shortly after Woodland Camo BDU's were issued.
Some A1 upper equipped carbines were issued with a 14.5" barrel, without the sould/flash suppressor, so that Snake Eaters and Rangers could wear OD green jungle fatigues and had a slight chance of being captured before they were shot, and it was still called the CAR-15.
Shortly after this, the carbine was equipped with an A2 upper and M4 barrel, and was only called the CAR-15 by Woodland Camo wearing dinosaurs.
Eventually the dinosaurs died off and the carbine become universally known as the M4, with the cool looking grenade launcher notch in the barrel, which you don't want to have if you give a damn about barrel harmonics, which, out to 250 meters, don't mean much.