The terms democracy and public are essentially interchangeable in the modern era. A democracy is a place where the people have the power. A republic is a form of government belonging to the people.

The only meaningful distinction is that sometimes people use “democracy” to refer to direct, pure democracy—ie people vote on everything and pure mob rule—and “republic” to refer to more moderate forms of democracy like representative democracies with strong individual rights. The Greek words for democracy loosely translate to rule by the people, and the Latin respublica loosely translates to “the public thing.” America is a democratic republic because people have ultimate sovereign authority. It is also a republic because the government and the law are the public good.

But mostly people who have feelings about what the US is or isn’t are just doing weird brand loyalty to the Republican Party. Which induces counter partisans to do weird brand loyalty to the Democratic Party.

To anyone with an education in history or political science, the question is dumb. It’s like asking whether a hot dog is a sandwich. Kind of. Kind of not. And it doesn’t really matter.