Of course the intermediate cartridge was alive and well before WWII. The .30 Carbine cartridge is an example. So is the 7.92x33 used in the MP-43. Of course the M43 Soviet cartridge (7.62x39) would not be an example of a cartridge used before WWII. The Mannlicher Carcano and Swiss Mausers used a 6.5, the Marines used a Lee Rifle in 6mm about the time of the Boxer Rebellion. The Spanish Mauser used against the US in Cuba was 7mm.
The Soviet M43 Cartridge has a muzzle velocity of about 2300 feet per second. That is nearly the same as the US .30 Krag (aka .30/40)
The M-1 Carbine was fielded by the US and the Germans captured some of them in 1942.
Germany, fielded their first prototypes of MP-43 in 1943.
The M-2 Carbine is fully automatic. Looks like the M-1, just as the M-14 looks like Springfield Armory’s M-1A. Difference is the selector switch.
The M-1 was designed to be select fire, between the wars. The initial issue was semiautomatic only. The US began issuing the M-2 Carbine, fully automatic, with a 30 round magazine in 1944. A T-17 or T-18 conversion kit converts the M-1 to fully automatic.
Very popular with the 101 and 82 Airborne, as you can schlepp a lot of ammunition.