Eugene Stoner designed the AR-10 for Armalite, in 7.62, then scaled it down to 5.56 and called in the AR-15. Armalite sold both designs to Colt. Colt then was able to sell some AR-15s to the US Air Force, and then it became standard for the US military as the M16. Colt made loads of that deal, though they had to pay Armalite some of it.*unboxes special pedantic hat*
I think the AR series is produced by Colt, so while the iconic weapons of the Old West (or the Dirty Harry movies) aren't being used, it is still a Colt weapon.
Armalite then designed the AR-16 (in 7.62) and AR-18 (in 5.56) as cheap export weapons for countries that couldn't afford the proper M16. Then the US bought lots of M16s from Colt, and gave them away to the potential buyers as military aid.
The patent has expired, and I read that a freedom of information act made the technical data package of the M4 (the carbine version of the M16) public domain. Also heard that someone at, I think, the Pentagon also accidentally leaked the M16 technical data package. Since the patent had expired, people could make their own if they knew how, but the companies don't have to give all the details (tolerances and stuff), so it's not that simple, unless the data package is available.
So everyone makes versions of the AR-15 (that is the semi auto version of the M16, which is the US military designation of the original select fire AR-15), and it's legal (providing they are allowed to make semi auto rifles, of course). Interestingly, in, I think, California, AR-15s are banned if they contain parts made by certain specific companies, but not others, cause US gun laws are rubbish.