Very Different
The cartridge difference is night and day.
The M1 Garand (.30-06) cartridge is unarguably a RIFLE cartridge.
It's large, it's heavy, it's undeniably manly.
The M1 Carbine (.30 carbine) cartridge is much shorter, is round-nosed, and is often confused with pistol cartridges. Gun writers even CALL it a "pistol" cartridge -- even though, if you fire it from a pistol, you'll quickly understand that it was designed for a (short) rifle. Fired from a 10-inch revolver, it produces a daylight-visible muzzle flash (some call it a fireball) and so much noise that only an auditory masochist would fire it without protection.
The Garand has serious power and range. A 600-yard shot with a Garand is only a matter of skill. The rifle has no problem with it.
The Carbine has better "firepower" meaning "practical rate of fire" which equates to the number of rounds you can put downrange in a given period of time. There's no 30-round magazine for the Garand, but there is for the Carbine.
For up close "social" work, the Carbine would be preferred. For long distance work and large game, the Garand would be preferred. You'll never take an elk with the Carbine, but the Garand has taken many.
The Carbine weighs about 6 lbs, while the Garand is closer to 10.
The .30-06 cartridge is available in many different loadings, and is a popular reloading cartridge, while the .30 Carbine has maybe 3 loadings and is a finicky cartridge to reload (so I'm told).
The Carbine is just plain fun. You can shoot it all day and not get sore. The Garand . . . has a little more umph. And the .30-06 ammo costs more than .30 Carbine.
I like the Carbine. I own one. It shoots minute-of-milkjug at 100 yards. I wouldn't put it up against kevlar, but for home defense . . . well, the round is as hot as a .357, so I'm okay with that.
I don't own the Garand, and have never fired one. All my data is from friends who have them and old codgers who carried them in the war. Like my dad. (He did say, however, that he preferred the Johnson.)
Lots of shooting, fun at the range, small to medium varmints? CARBINE.
Hunting, long range shooting, fearsome sidekick, real power? GARAND.