the way i see it, a republic is a country without monarch (so no hereditary power), a democracy is when a country is ruled by the people or their representatives.
So if the ruler of a country is only chosen by a handful powerful people, i wouldn't consider it a democracy but i would consider it a republic.

The line between definitions is definitely thin. but in a practical sense not every republic is a democracy. they might say they "rule for the people" but de facto it ends up being a tyranny/autocracy

republic just means there is no monarch, noth korea is also (still) considered a republic although the current leadership is starting to look a lot like a monarchy