I'm writing a bit and ran into a problem when denoting rules for an area, and it got me thinking on if the titles were correct.

As far as I have guessed, Emperors are conquerors and Kings are done by family/divine right, is this correct? What would be the main difference between denoting an Empire and a Kingdom? or a Principality for the matter.

Beyond that, I ran into [this picture] (http://www.hierarchystructure.com/wp-content/uploads/2012/07/Royal-Family-Hierarchy.jpg) denoting a hierarchy of noble titles, but could this be organized in the same way a President -> Governor -> Mayor is organized? or are the titles much different and dependant on other things beyond size of the territory granted?

Thanks a ton for the help