in American English the word, "country" and "nation" are completely exchangeable. they mean the same thing.
Have to say I disagree. "Country" in the relevant sense is a geo-political entity. "Nation" refers to a group of people. These needn't precisely coincide. This tends to be more apparent in developing countries, but to give a closer-to-home example, there's the "Cherokee Nation." "Cherokee country" would be something quite different.