Tri bike vs Road bike

I'm going to expose my complete newbieness, but here goes anyway.  What is the difference between a tri bike and a road bike?  I presume it has to do with the way your body is held while you are actually riding, and I further presume that my local bike shop would be able to help me out, but I'd like to have some idea of the answer before they try to sell me a new bike.  I already have what I believe to be a good road bike, and an old mountain bike that I love, even if it does not have shock absorbers.