Not OP, but I don't understand your question.

As a US citizen, I try to say "The States" instead of America when talking about my country. I do that out of respect for all of the countries that call these two beautiful American continents home.

I admit to defaulting to "American" instead of a cumbersome "United Statesian" or the above "US Citizen." But that's what we grew up calling ourselves and told to call ourselves and our fellow countrymen.

"Just another American Country" seems like it would be insulting to Canada, Chile and all of our neighbors in between. I'm not sure my fellow Americans would even pick up that you were talking about the States unless you really layed on thick context.