Is the United States a democracy or a republic?

The two terms answer different questions. Democracy describes where power originates, with the people, and a representative democracy means citizens exercise that power by electing officials rather than voting on every measure directly. Republic describes the form of the state, one with no monarch, where officials hold office through election and govern under law. The United States is accurately called a constitutional republic, a representative democracy, and a federal republic, and none of these contradict each other, which is why serious political scientists use them together rather than treating them as rival categories.

The it's a republic, not a democracy line usually appears in arguments about majority rule, and the underlying point it gestures at is real: the American system deliberately constrains simple majorities through a written constitution, individual rights that majorities cannot vote away, an independent judiciary, federalism, and structural features like equal Senate representation and the Electoral College. Those are meaningful design choices worth debating on their merits. But framing it as a terminological correction is not accurate, the founders used both words, sometimes idiosyncratically compared to modern usage, and the US government's own materials describe the country as a democracy. The honest response is that the country is both, and the substantive disagreement is about how much majoritarian decision-making the system should permit, which is a question about design rather than definitions.