Quote Originally Posted by Kmcmichael View Post
Fair enough, a republic is governed by the rule of law i.e. A constitution.
A democracy is governed by the votes of the people.
This isn't enough of a distinction to warrant comparisons, because of the big overlap between these two categories.

Which you noted with:
Quote Originally Posted by Kmcmichael View Post
The US is a democratic republic as it has elements of both.
Quote Originally Posted by Kmcmichael View Post
The term representative democracy is redundant as is constitutional republic
I am not quite sure about this. A direct democracy is different from representative democracy. In the first you chose representatives to make decisions on your behalf, in the second everybody votes on every decision.
And I don't see why a republic needs to have a constitution which is the overarching framework. Couldn't you simply make laws as it is necessary? Governing by written law, as opposed to say the judgement of appointed or elected officials doesn't seem to require a constitutional framework.
For example, what was the constitution of the Roman Republic? As far as I know there wasn't anything formal like in the USA but precedents and principles evolved over time. I think that form of government is still considered republic - it succeeded a monarchy and was followed by empire (in many ways a monarchy).