I think my point, if that's not too grand a word, was that North America is a continent while Central America is a region.
Whether all or part of Mexico is included in Central America seems to be entirely a matter of personal choice.
North America goes all the way down to somewhere around the border between Panama and Colombia.
"Northern America" may or may not include parts of Mexico, depending on what definition you use. Wikipedia helpfully informs me that it's just above Middle America though.