The US is not a democracy?

I am listening to the The Connection on North Country Public Radio this morning and their phone-in/interview of Roy Moore, the former Alabama Chief Justice who placed a block of stone with the Ten Commandments on it in a courthouse.   During one call, I heard a most extraordinary statement, that the United States is not a democracy but a republic. Quick recourse to Google linked me to this discourse on the distinction. I always considered a republic a sub-set of democracy just as is our Canadian constitutional parliamentary monarchy. Was I wrong?