Today, we have a mixed form of government with a strong element of popular or majority rule. Jefferson would call that element “republican”; many people today would call it “democratic.” No one, then or now, would assert that we have a pure democracy. In the social studies framework, we called our system a “constitutional democracy” to indicate that the powers of the people are checked. The government is not in “direct and constant control by the citizens.” [Likewise, the powers of the federal government are limited.]
How did this semantic ambiguity arise? The word “democracy” is of Greek origin. It literally means “rule of (or by) the people.” One could hold that the sovereign power in the US is the people–and hence we have a democracy in the etymological sense. Like all old words, however, “democracy” has accumulated resonances beyond its etymological origins. It may invoke the Greek city-states (whether seen as ideals or as disasters) or mass modern societies.
“Republic” comes from the Latin. My Latin dictionary says that “publicus” means “belonging to the people.” Thus “res publica” means the “thing belonging to the people,” whereas “democracy” is the “people’s rule.” If there is a significant difference in the etymological sense of these words, it is the difference between something that the people have (a republic) versus a power they wield (democracy). A better translation than “the public thing” is “commonwealth.” The words “republic” and “commonwealth” invoke the Roman regime before Caesar Augustus, the Cromwellian state, the early American colonies, and the ante-bellum US system. The meaning of “republic,” however, is malleable, because it depends on which features of the Roman republic and its descendents one considers definitive.
Ultimately, the United States can be called republican and democratic. The two words have interestingly different origins and resonances but are not sharply distinguishable. Nor do we have either a pure republic/democracy. Some limitations on the republic/democratic element are wise, but our current system is flawed by most standards. Although our democratic/republican aspirations are only partly realized, they remain beacons.