My dad told me he frequently carried a M2 full auto carbine in Korea. But I always thought they were .30 cal. (Not 30-06 like the M1)
The Army, in their infinite wisdom named the M1 Rifle and M1 Carbine with the same designator.
Yes, your dad's M2 Carbine (which is a full auto variant of the M1 carbine) fires the .30 Carbine round, which is a lot less powerful than the M1 Rifle's .30-06 round.
Carbines were .30 cal. The garand is a 30’06 rifle. My uncle in Korea carried an M1 carbine that was full auto. He was in the 24th division and saw heavy fighting in the summer of 1950 being the first unit thrown into the fight. He liked the M1 Carbine.
If I were going to go .30 cal carbine ammo wise I would get the 110 grain hollow point round way better than ball fmj. And expect to pay more for a .30 cal shooter, especially if you go M1 carbine route.