Thanks to a link at the Volokh Conspiracy here is a five minute overview of the difference between a democracy and a republic:
Aristotle did not think much of “democracy,” because “A democracy is rule by the poor, because there are so many of them.” While there are fewer poor in the sense Alexander the Great’s tutor thought of poor, there are plenty who think they are poor. And you can depend on those to vote themselves largesse from the public treasury until the nation has consumed itself by the excesses of its rulers. Something democracies share with monarchies.
Aristotle did not think highly of republics, either. “A republic is a political scheme in which the great masses of the people are armed, that they may rush to the common defense; while the rulers command no more forces than are needed to govern the state.” Something both monarchies and democracies abhor.
While our Republic adds a layer of representatives between we the people and the acts of the government, it works. And, unlike every other form of government, our Republic was not formed with fear of the people as a basic precept. We the people had a God given right to be armed, and an Amendment was not necessary to protect that right. I am thankful those with a longer view of human evil prevailed and we still have that right to keep and bear arms.