But not a decidedly different thing from a representative democracy.
There is nothing magical or sacred about a republic. To wit: The REPUBLIC of Cuba, The Union of Soviet Socialist REPUBLICS, The People’s REPUBLIC of China, The Islamic REPUBLIC of Iran, The Socialist REPUBLIC of Vietnam.
Any excrementhole state can call itself a “republic.”
First, I am fairly sure the government that uses representative democracy is called a Republic. A classic Republic was Rome but it did not have a Constitution to limit the representatives. The founding fathers decided to add a Constitution to severely limit what the federal government could do. Of course, it only works if the representatives follow it. THus, the US’s federal government is a Constitutional Republic which is executed in representative democracy, at least in part.
Concerning misuse of words, anyone can start using a word to mean the opposite of what it is defined to mean which is your point about the misuse of the word republic today.
The word liberal was changed about a hundred years ago when leftists started taking over our federal government. I call myself a classic liberal but if I use that term today, most people will conclude I am a democrat, progressive or leftist when in fact, i am the exact opposite.
Here is a Friedman video on classic liberalism.
https://m.youtube.com/watch?v=QmeeMYrnweg
JoMa