Notes

A personal union is when a single ruler/monarch may control two or more independent/sovereign states at once, where the states remain distinct in their borders, laws, etc. A subsidiary title is a hereditary title (inherited across family generations) but is rarely used to refer to the person holding the title, since they at the time possess a greater title by which they would be referred to. So, for example, if you were the Duke of X and also the Count of Y, you'd likely be referred to as the Duke of X considering that it is a greater title.

As it turns out, there are various monarchical titles. The three levels of monarchs are emperors, then kings, then grand dukes (see later, dukes also included and also likely archdukes). A grand duke controls a particularly mighty grand duchy, however, the grand duchy is not large or powerful enough in order to be designated as a kingdom. Likewise, a king/queen are the monarchs of kingdoms, however the kingdoms are not large or big enough to be considered an empire (and if it grows to that size, a change in title can occur, as happened with the eventual transition of the Roman Kingdom to, through the period of the Republic, the Roman Empire).

As for a duke, a duke can either be a monarch, or be the highest rank directly below a monarch (belonging to the nobility/royalty). It depends. The Duke of Lotharingia was certainly a monarch, for example, whereas the Duke of York, not so much.