Interesting. I only know 2 models of geography that consider North America a continent, the rest treat America as a continent. I guess this is no different than people calling United States of America "America". I wonder what citizens of the countries in North or South America think about it. UPDATE: my comment got downvoted. I wonder why
Can you talk more about what models of geography you're referring to? In school in the US, I was always taught there were 7 continents, including the North and South Americas as 2 separate ones. As far as I remember, there was never even a mention of other models apart from maybe some historical understanding before lands had been fully explored by Europeans.
I was never really taught a different model either, but the entire distinctions always felt strange. Moreso with Eurasia.