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Oftentimes people use the phrase "the American people" as if it were a single monolithic group of clones of some type called American, whereas, in fact, each individual person is different from every other person, not just in America, but everywhere. I treat the phrase as a red flag for group-think, i.e., collectivist/statist thinking.
On the rare occasions I talk about American people as a distinct group, I say just "American people" to emphasize the plurality, without the article, which can collectivize the phrase.
FYI, American people ARE different from Canadians, Africans, or Middle Easterns, or Japanese, as each of those groups is different from the others, and each member of those groups is different from all the others, but not in any significant way. Different local history, geography, and traditions and customs, but not e.g. different species.