Wiki gives a good explanation of what a real M14 is:

M14 rifle, officially the United States Rifle, 7.62 mm, M14,[5] is an American selective fire automatic rifle that fires 7.62×51mm NATO (.308 Winchester) ammunition. It gradually replaced the M1 Garand in U.S. Army service by 1961 and in U.S. Marine Corps service by 1965. It was the standard issue infantry rifle for U.S. military personnel in the contiguous United States, Europe, and South Korea from 1959 until it was replaced by the M16 rifle in 1970.[6] The M14 was used for U.S. Army, Coast Guard and Marine Corps basic and advanced individual training (AIT) from the mid-1960s to the early 1970s. The M14 was the last American "battle rifle" (weapons that fire full-power rifle ammunition, such as the 7.62×51 mm) issued in quantity to U.S. military personnel. The rifle remains in limited service in all branches of the U.S. military as an accurized competition weapon, a ceremonial weapon by honor guards, color guards, drill teams, and ceremonial guards, and sniper rifle/designated marksman rifle. The M14 serves as the basis for the M21 and M25 sniper rifles.****

That being said. A few manufacturers, SEI being the main example, make semi-auto variants of original M14. They are stamped M14 so would technically be M14 regardless of the bullshit semantics people in the sub want to bring up (if it's named M14 then it is M14). Others such as LRB name their models M14S. The only difference in these rifles and the original M14 is the select fire ability. They're simply missing ~3 pieces.

The M1A is what springfield name's their version of the semiauto M14. People get their panties in a bunch about springfield's poor quality, but the truth is that base fulton, lrb, or sei rifles even to USGI spec aren't going to group any better than a springfield m1a. You will only get a sub moa accuracy from a pieced together and accurized semi auto m14 variant that you have made from the best parts available (national match and superior quality, mostly SEI and sadlak parts with kreiger barrel). That does get extremely pricey and you'll be in close to $5K to get a submoa semi-auto m14 variant.