The .410 has been at various times marketed as both a 36 gauge as well as a 12mm. Both designations are of course incorrect. 36 gauge = .506" diameter. 12mm = .472" diameter, or about the size of the head of the shell, no other sizes of shotguns are so specified, always the bore diameter.
.410 is actual decimal size, not a gauge as such & it measures "Guess What" .410". This is the nominally correct size for a .410. Manufactures could of course apply their own thoughts to the actual size used as well as they had manufacturing tolerences. A bore of .400' = 72.68 gauge & one of .420" = 62.78 gauge. ±.010" should cover most variations of a .410 "Caliber" shotgun.
The "Gauge" of a barrel having a bore diameter of .410" = 67.49