I know that a lot of people use the term North America loosely to just refer to Canada and the USA, but didn't they ever learn the continents of the world at school?

Geographically, North America ends at the Panama Canal. Below that you have South America. Central America is a term used for the Southern part of North America, and Central America combined with South AMerica gives you Latin America.
Either way, if you look at how FIFA divides the world, they follow the continents. There are federations for Africa, Asia, Oceania (aka Australia, but I guess the Kiwis prefer the other term....), Europe, South America - and then there's Concacaf....
For some reason there is no federation for the Antarctica.
Anyway, since it is obvious that they have divided the world according to the established continents (some modifications though, Israel is part of UEFA rather than having to face all their Arab neighbours in World Cup qualifications

, and Australia actually switched to Asia a couple of years ago, which makes it really lucky that the Oceania division goes by that name rather than the alternative ), it would be logical to just use the traditional name for the North American continent rather than adding a number of subdivisions to the name.
But I guess people just don't know geography any more.
I've seen ads for trips to "Europe and Scandinavia" which makes just as little sense.