Only if you believe "violet" and "mauve" are both the same thing, because they both mean "purple".

Look, I'm a descriptivist, but my point is that there is nothing about the word "Republic" than implies representative democracy more than "Democracy." This distinction boils down to Federalist No. 10, when Madison uses the two terms differently... but he specifically says he's using these terms in a technical way to make a point:

>A republic, by which I mean a government in which the scheme of representation takes place, opens a different prospect, and promises the cure for which we are seeking. Let us examine the points in which it varies from pure democracy, and we shall comprehend both the nature of the cure, and the efficacy which it must derive from the union.

>The two great points of difference between a democracy and a republic, are first, the delegation of the government, in the latter, to a small number of citizens elected by the rest; secondly, the greater number of citizens, and greater sphere of country, over which the latter may be extended.

He's using affected meanings, and he's going out of his way to say "varies from pure democracy" before referring to "pure democracy" as "democracy." Why is he doing this? Because the words mean the same damn thing!

People who are distinguishing them here are relying on peculiar definitions of these terms, which are largely peculiar to Americans-and I’d add, only some of them.

To an Australian or Briton or Canadian or New Zealander, “Republic” means not being a constitutional monarchy. I think it means something similar in a lot of other countries. Australia is a democracy but not a republic, because it has a King instead of a President. The US, France, Germany, Ireland, Israel (putting aside the Palestinian issue) are democratic republics, because they are democracies with Presidents instead of a King/Queen. China or North Korea are republics but not democracies; Saudi Arabia is neither a republic nor a democracy.