This concept is extremely difficult to explain to kids, of which I have 2 daughters and have made the difference clear. When you have Republicans like Cantor and others use the “d” word, they’re like...”Dad is smarter than Eric Cantor”?!
Indeed it is used too loosely!
Could it be said that we have a “democratic republic”, where the majority elect representatives to legislate?
It is pretty difficult to explain to adults as well. A few months ago I tried to explain this to the Oregon Freeper Thread and was soundly criticized as they demanded that we (the USA) is a true democracy.