The original design of the weapon was the AR-15, and it was fully automatic, as was its predecessor design, the AR-10, a 7,62 NATO military rifle, also full-auto. The Army Limited Warfare Laboratory purchased several thousand for the Army Special Forces around 1961, as did the US Air Force, looking for an individual airfield defense weapon and aircraft guard weapon to replace the leftover WWI M1 and M2 carbines then being used for that purpose. The first reifles to see combatr in Vietnam were the original military AR-15s, which after modifications by the Army Ordnance branch meant to make the weaopon more suitable for general troop issue, was designated XM16, then adopted in 1967 as the M16.
It was around 1964 that the civilian-legal AR-15 version was developed, then designated the SP-1. They sold for around $200 each at the time, for which you could buy three M1 Garands. I got my first SP-1 in 1965.
AR-15 is the Colt registered trademark for the ubiquitous civilian version of the military M-16 rifle. The key difference is the civilian version fires only semiautomatic.