The difference between a democracy and a republic is not just semantic. Democracy is just majoritarian rule. It is the rule of what three wolves and a lamb decide to have for dinner. Aristotle divided governments into three categories, those ruled by a single person, those ruled by an elite, and those ruled by the general population. For the first two he divided them into pure forms and debased form: monarchy vs despotism; aristocracy vs oligarchy. But he saw no pure form of democracy, it was always a debased form that led to tyranny. Rather, what he advocated was polity or a republic where the three sources of power—monarchy, aristocracy, and popular—would be balanced against each other. This was what our founding fathers were trying to establish. Pure democracy frightened them.
Democracy is two wolves and a sheep voting on what’s for dinner.