A perennial question from students, citizens, and politicians is “are we a democracy or a republic?” Usually the questioner is hoping to hear “democracy” if they currently identify as a Democrat or a “republic” if they identify as a Republican. That’s wishful thinking.
Robert Dahl on pp 16-17 of ON DEMOCRACY blames James Madison for causing this confusion. Dahl writes “the plain fact is that the words democracy and republic did not (despite Madison) designate differences in types of popular government. What they reflected, at a cost of later confusion, was a difference between Greek and Latin, the languages from which they come.”
In Federalist #10, Madison distinguishes between “a pure democracy, by which I mean a society consisting of a small number of citizens, who assemble and administer the government in person” and a “republic, by which I mean a government in which the scheme of representation takes place.” In the U.S, we have features of each. Compare, for example, citizens voting on tax and bond issues with a life-long tenure of judges nominated by the president with the advice and consent of the Senate.
In modern parlance, it would be clearer to use “participatory democracy” and “representative democracy” and get on with promoting “rule by the people” or Lincoln’s “a government of the people, by the people, and for the people” rather than fish for a rhetorical advantage.