@Ross at Play
I still "prefer" to use The Americas. To me, it identifies a combination of two distinct units, which geologically they are. It also has the advantage of being unambiguous in all circumstances.
When I was at school they used the term Americas to refer to - North America (Canada, Mexico, & USA), South America (Colombia, Venezuela, plus all points south of them), and Central America (Guatemala, Nicaragua, Costa Rico, Panama) - I still think of them that way. Which is why I try to avoid the term America since there really isn't an America as such. Kind of like there's a North Dakota and a South Dakota but no Dakota.
edit to add:
The USA isn't the largest country in North America, Canada is by over 100,000 sq kms - Canada 9,984,670 total sq kms - USA 9,833,517 total sq kms. The USA has 323,995,528 people est as July 2016 - Canada has 35,362,905 people est as July 2016 - the USA just has more people in it. Those figures are from the CIA book of facts and I'm not sure if the population counts includes illegals or not.