CLICK HERE for the history of the M16 rifle.
NOTE: Over the years, "AR-15" (AKA AR15) has become the common-usage name of the semi-auto civilian version of the M16. When Eugene Stoner of ArmaLite created the select-fire full-auto / semi-auto military rifle, he designated it the AR-15. COLT bought the rights for the original AR-15 from ArmaLite and it was rebranded the M16 by the military. AR stands for ARMALITE; it does not stand for AUTOMATIC RIFLE. Colloquially, AR has taken on a patriotic connotation as standing for America's Rifle; so be it.
I believe Colt still owns the marketing rights of branding any rifle as an AR-15.