I don't know about the OFP version, but the real M14 was originally both semi- and full auto. However, the full auto function was deleted, because the heavy recoil made it so inaccurate. The M1A is a post-war commercial version, semiauto only.
BTW, the M14A1 was a light machinegun version. It was essentially a full auto M14 with a heavier barrel, bipod and pistol grip.