Canadians, Brazilians, Argentinians, Mexicans, etc. are all Americans, since they all are from 'America'.

The bit about Louisiana, what I'm trying to say is since the USA co-opted the name 'America' for the country, you can't call the south of your country 'south America' or the north 'north America'. It's confusing!! So you just go by 'The South' because 'America's South' or 'American South' is confusing as well!