The 2nd type is known as the "M1 Carbine" which fires a smaller, .30 cal. round.
The M14 fires the 7.62 mm NATO round, the same as the M! Garand.
However, the gun will fire any round with .30-06 or .308 dimensions if the pressure profile is a good match. I had my Garand refurbished and rebarreled in .308/7.62 NATO, and it was quite reliable. The Navy started doing that sort of thing the earliest that I know of, with a sleeve fitted into the chamber (!).
What's the farthest shot you've heard of from credible sources?
Normal Garand match ammo, at least the typical Federal .308 (don't know about .30-06) Sierra MatchKing match loads, are supposed to have real difficultly reaching 1,000 yards. If you want to stay in the envelope it's recommended to go down to, say, 6.5 mm bullets, a diameter where you can get much higher ballistic coefficients, e.g. the .260 Remington and its ilk.
Note this is all stuff I've just read, I've never been at a range that was longer than 300 yards, and almost always 200 or less.... :-(.
With information from http://en.wikipedia.org/wiki/M14_rifle:
The M14, while "developed from a long line of experimental weapons based upon the M1 rifle" (a semiautomatic rifle which certainly saw widespread use in WWII), did not enter production until 1959. Compared to the M1, the M14 was fully automatic rather than semi-, had a much larger magazine size, shot a different bullet, and was actually significantly lighter -- so even knowing nothing about how the actual mechanism and whatever other properties of a gun that impact its performance were changed, it's safe to say it's not the same gun, and this is a factual error.
The fact that, as someone who has never even seen an unholstered gun outside a museum much less shot one, and has no domain knowledge outside of movies and a single decade-old video game, I could spot this error from a mile away, makes me skeptical about this article. I know this seems like useless nitpicking, but it reminds me of reading mainstream articles about relatively esoteric high tech subjects: in domains I know better, these articles are often so nakedly full of holes and errors that they totally waste whatever argument the author is working towards. So whenever I spot easy errors on topics I know little about, it puts me on higher guard for what else might be bullshit that I don't recognize.
That said, this is a fascinating article, and even with skepticism it has adjusted my perspective on the debate.