M-14 does not necessarily mean it is a full auto. There are plenty of manufacters out there that make Semi Auto M-14s. Fulton, Armscorp, LRB, Norinco, Polytech to name a few.
There is no difference between a semi M-14 and a M1A. REPEAT: NO DIFFERENCE BETWEEN A SEMI M-14 AND A M1A.
The term M-14 is applicable to all M-14 type rifles. Springfield Armory wanted to not be known as another company to sell a M-14 type rifles so they decided to market their rifles as "M1A". Pretty smart marketing move if you think about it. So there than that, both rifles are pretty much identical.
Now there are some select fire M-14 rifles, but they are pretty rare and come with a hefty price and a ton of paperwork.