Correct, the receivers are identical. However, if a receiver is stamped 'M2', it is legally a machine gun even as a stripped receiver. Starting in 1945, the roll stamp on the receiver stopped at ' U.S. Carbine Cal. 30 M ' to allow the individual receiver to be stamped with a 1 or a 2.
Further muddling the mix, many receivers stamped 'M1' were converted and registered as a machine gun, which makes that particular receiver legally a machine gun even if there are no MG parts on it, because according to the ATF, "Once a MG, always a MG".
Making the overall situation even MORE confusing, many of the parts that are unique to the M2 were installed on semi-auto M1 carbines at the factory: hammer, sear, slide, stock, trigger housing, magazine catch, and sometimes even the disconnector, leaving only the selector switch and the disconnector arm as the only pieces that kept if from being a MG.