In a Democracy the people are the source of both the power and the authority, creating an emphasis on a system of majority rule. So in a democracy if the majority arbitrarily decided to outlaw Santa Claus, nuke the dolphins, and institute a national dress code requiring everyone to shave their heads and wear only one shoe -- well, that's what would become law. Because that's how a Democracy works.
In a Republic the people hold the power, but the authority rests in the Law. Which makes a surprisingly BIG difference. It means that there is a higher power, some ultimate authority greater than the will and whim of the people.
At the founding of the United States the moral authority of the Christan Bible was widely recognized and understood as the LAW upon which our government was founded. (There's plenty of proof on this point if anyone bothered to actually read it.)
When we have shaken off the last vestige of Christianity, when we have abandoned even the Ten Commandments, when we are no longer responsible to a higher authority -- then we will be a Democracy.
And in that day when the majority rule becomes that ultimate arbiter of right and wrong, the majority may decide to outlaw Santa, may decide that Thou SHALL Kill... might declare it unlawful to wear matching socks, or eat oatmeal cookies, or have a vegetable garden... may decide to reinstate slavery, or institute martial law, or seize corporations as government assets, or abolish the institution of marriage...... because that can happen in a democracy. But we were never supposed to be a democracy.
I pledge allegiance to the flag and to the REPUBLIC for which it stands, one nation under GOD, indivisible, with liberty and justice for all.