What are the differences between a democracy and a republic?

A republic is a representative democracy, where the people elect representatives to make laws for them. A republic makes decisions democratically by the majority vote of representatives.

In a representative democracy you elect a few to represent you in the decision making, and make decisions for you, rather then you yourself vote on every decision.

(The United States is a republic, or representational democracy, because the people vote for representatives to represent their views in congress. James Madison defined republic in terms of representative democracy as opposed to direct democracy.)

A direct democracy, or pure democracy, is where the people rule directly, voting on every law themselves. It's a form of government ruled by majority of every individual. A direct democracy allows all citizens to vote on every decision.

Direct democracy is where citizens vote directly by ballot to make decisions for the government. Direct democracy originated in Athens.