The Difference Between a Republic and a Democracy

I found this article today and, while I was reading it, certain affirmative phrases kept running around my head. Stuff like: "Right on!", "You tell 'em!", and "Give 'em hell!"

My problem has been, everyone seems to either use the terms Republic and Democracy interchangeably, or they have been so brainwashed by our public school system that they actually think that our government is supposed to be a democracy (these same people haven't ever heard the term republic in their lives - I think it has been banned from school textbooks). So if you are one of those people and would really like to know what I mean by "republic," or you just want to see why I was going through so much affirmation while I was reading the article, check it out. I promise you, it is worth your time.

Republic? Democracy? What's the Difference?