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.... :-(.
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.