Was there ever an official definition for what is a kingdom, empire, duchie and other similar terms?

by Ajavisk

We hear a lot about x empires and y kingdoms, but what was there ever an actual definition for what diferenciates them? If there was not, how was the terminology chosen?

amisslife

Just to add on to this question: why is it the Grand Duchy of Luxembourg, and why were the Hapsburgs so often called Archdukes? What was the difference between a Grand Duke, an Archduke, and a duke/king/prince? What was the level of consistency with which these titles were applied across the various monarchies around Europe? Was there a consistent hierarchy of prestige (i.e. was the title of Grand Duke *always* more prestigious than being a prince)?