From the 1828 (first edition) of Webster's dictionary:
> Republic: 1. A commonwealth; a state in which the exercise of the sovereign power is lodged in representatives elected by the people. In modern usage, it differs from a democracy or democratic state, in which the people exercise the powers of sovereignty in person. Yet the democracies of Greece are often called republics.
So historically, a distinction was in fact made.
Here is Alexander Hamilton (a republican in the classical sense of the word) making the distinction very clearly:
> "We are now forming a republican government. Real liberty is neither found in despotism or the extremes of democracy, but in moderate governments. Those who mean to form a solid republican government, ought to proceed to the confinges of another government. As long as offices are open to all men, and no constitutional rank is established, it is pure republicanism. But if we incline too much to democracy, we shall soon shoot into a monarchy."
What we in the US have is a representative democracy / republic that is also rather decentralized federation (states and state's rights) as well.
The US is a democracy. πΊπΈ