The M1 turned into the M14 around the late 50's according to this M14/M1A book I had. It started off as the T44 I believe and went from there. The M14, basically has the capability of fully automatic fire, like was the case with the squad light machine gun version they had. It had a bi-pod on it, and fired in fully automatic. At the time, the Army kind of deemed it a "worthless" creation9M14A1). The M1A is basically you're civilian style, as you said the M16 to AR15 type. As far as the M14 history goes, it beat out the Belgians T48 (basically the SA58) to eventually be our battle rifle. Honestly to this day, we'll NEVER have a true BATTLE RIFLE that will be what the M14 and the M1 Garand were.
If you place an M1 Garand and M1A/M14 side by side, the same features are really the bolt, sights, and you could say the walnut stock. The M14 came with a flip up butt plate (which I loved) for added stability during fully automatic fire. That's one added benefit where the M14/M1A design start to differ other than the obvious magazine fed vs. box mag fed from the top Garand style.
2 Versions of M14
http://tri.army.mil/LC/cs/csi/m14rifle.jpg
There are tons of M1A versions out there from Springfield, but traditional M14's were produced by companies like Winchester, TRW, Remington, and Harrington & Richardson Arms Co.
Here's some factual and not bad info from Wikipedia suprisingly: http://en.wikipedia.org/wiki/M14_rifle