Here is picture to get things to scale:
All three use 7.62 mm diameter bullets but case sizes and shapes are dramatically different.
The .30-30 was a sporting hunting cartridge for lever action rifles.
The .30-06 was an early rimless military design that was used in 1903 Springfield v2 and the M1 Garand.
The .30 Carbine was originally used in the M1 Carbine.
Here is an M1 Carbine and an M1 Garand:
And a 94 carbine reproduction: