[DanaC]

I think our conception of the term 'democracy' has shifted somewhat over the last hundred years or so. Rather than meaning mob-rule, it now has connotations simply of increased participation in the governance of the Nation. Republic and democracy have become more or less interchangeable, because Democracy is one of the ways in which Republic can be sought, and Republics have at their core a system of participatory governance which is democratic in nature: every citizen gets to vote in local and national elections, but every governmental decision is not put to the vote.

From Tom Paine's Rights of Man:

The only forms of government are the democratical, the aristocratical, the monarchical, and what is now called the representative.

What is called a republic is not any particular form of government. It is wholly characteristical of the purport, matter or object for which government ought to be instituted, and on which it is to be employed, Res-Publica, the public affairs, or the public good; or, literally translated, the public thing. It is a word of a good original, referring to what ought to be the character and business of government; and in this sense it is naturally opposed to the word monarchy, which has a base original signification. It means arbitrary power in an individual person; in the exercise of which, himself, and not the res-publica, is the object.

Every government that does not act on the principle of a Republic, or in other words, that does not make the res-publica its whole and sole object, is not a good government. Republican government is no other than government established and conducted for the interest of the public, as well individually as collectively. It is not necessarily connected with any particular form, but it most naturally associates with the representative form, as being best calculated to secure the end for which a nation is at the expense of supporting it.