Personal union

A personal union is the combination of two or more states that have the same monarch while their boundaries, laws, and interests remain distinct. It differs from a federation in that each constituent state has an independent government, whereas a unitary state is united by a central government. The ruler in a personal union does not need to be a hereditary monarch.

Personal unions can arise for several reasons, ranging from coincidence (a woman who is already married to a king becomes queen regnant, and their child inherits the crown of both countries) to virtual annexation (where a personal union sometimes was seen as a means of preventing uprisings). They can also be codified (i.e., the constitutions of the states clearly express that they shall share the same person as head of state) or non-codified, in which case they can easily be broken (e.g., by the death of the monarch when the two states have different succession laws).

The Commonwealth realms are independent states that share the same person as monarch.

Because presidents of republics are ordinarily chosen from within the citizens of the state in question, the concept of personal union has almost never crossed over from monarchies into republics, with the rare example the President of France being a co-prince of Andorra.

Even though France is now a republic with a president and not a monarchy, it has nevertheless been in personal union with the neighboring nominal monarchy (non-hereditary) of Andorra since 1278.

For more information, see § Korea: Goryeo below.

In 1102, after a period of succession crisis following the death of King Demetrius Zvonimir, the Kingdom of Croatia entered a union with the Kingdom of Hungary in 1102. The crown passed into the hands of the Árpád dynasty with the crowning of King Coloman of Hungary as "King of Croatia and Dalmatia" in Biograd. Institutions of separate Croatian statehood were maintained through the Sabor (an assembly of Croatian nobles) and the ban (viceroy). In addition, the Croatian nobles retained their lands and titles. Some of the terms of Coloman's coronation are summarized in Pacta Conventa by which the Croatian nobles agreed to recognise Coloman as king. Although it is not an authentic document from 1102 and is likely a forgery from the 14th century, the contents of the Pacta Conventa correspond to the political situation of that time in Croatia.

...
Wikipedia