I don't use Romex much, so I didn't know there was a "3/8" NM connector. I just know them as Romex connectors--regular (fits in 1/2" trade size KO) and "bigger"--fits in 3/4" KO. I know BX/MC connectors are called 3/8", and I figured it was because the same connector can be used for 3/8" flex. The one you have pictured looks like it's for under-cabinet strip fixtures.