Redbilled, blackbellied? North and South? It does not refer to the American continents, but to the geographic variation of the ducks as they occur.
Of course, birds in the wild that fall in love won't mind if their beloved one has one brown feather more or less. So in reality there will be a huge variation of birds, going from the almost grey breasts to the browns with slight grey board. Who decides where the birds are southern or northern, I don't know. The only thing we can do is look for the extreme ones in our collections.
All the 'in between' birds are just as good. They should be passed on as redbilled. Only when you are close enough to the north of south version, add that to the name.
Young Aviornis members once started a project to keep the real North ones going. We still have some descendants from these original birds.