Republic: The terms is used by the Romans to describe their governmental system. Today it is commonly used to denote a government of popularly elected representatives, like congressmen or senators in the US.

Democracy: Greek term for rule by the people. As it was practiced by the Athenians, democracy meant that the assembly of all citizens controlled the political life of the city. Anyone could speak in the assembly, and proposed laws and resolutions were openly debated. Most magistrates were appointed by lot. Election was considered undemocratic (who else would win but the rich and the famous?). Other Greek cities practiced a more moderate form of democracy, in which elections were more common, and in which a smaller council (boule) decided what was to be proposed to the assembly.

Even in the ancient world, both terms were often vaguely employed to mean "good government." During the Hellenistic period, it was possible for cities to pledge to protect each others "democracies" when the government of neither city was, in fact, democratic. In these cases "democracy" merely meant something like "the city's laws." Republic literally means "the public affairs." It was and can be used to describe a wide variety of governments. The senators of the Roman Republic, for example, were not elected to the office of senator, nor did they represent any particular group of people, though election and representation are both standard elements of our definition of a republic. The ancients perceived a difference between the Roman constitution and Greek democracy. But at the same time, it was the ancients themselves who first used both terms loosely and introduced the vagueness that allows us to use them both more or less interchangeably to mean free government.