In school we were told that in a kingdom you have king (sometimes a queen) who gets the job by birth and in a republic the president and/or the prime minister is chosen by the voters.
At those happy times nothing was ever said about those strange hybrids we can see nowadays, in many countries.
First, you have the species called "President for life". You get the top job and you keep it. Sure, there are elections, but................... A good example is Egypt.
Second, like in a good old kingdom the little one succeeds papa. As far as I know, there are two countries Syria in the Middle East and North Korea, just above South Korea.
Those two, however, play in different leagues. When papa died in Syria, the son was an eye doctor in London and I imagine it was not that easy to adopt. But he made it and it appears he has learned his trade and is doing quite well. In North Korea the succession to the "throne" was further hampered by the fact that the country is a communist one . Till now, the commies always killed their last king - when they could get him - or sent him and his family into exile.
Thus I think North Korea merits amply our admiration, they established the first communist monarchy.
Once you have a royal family in a country you get the aristocracy into the bargain. Or the other way round. The nobles choose the king among them. But there is a big republic - the United States of America - where the top jobs seem to be family business. In this country the family president is not called George I and George II but modestly - it's a republic - N° 41 and N° 43.
And in this family pool is another fish swimming who might be one day.......... For the moment, he is just governing a subtropical southern state of the Union.
All this can be called happy diversity of human behavior. It enriches us and them.
I should have added a photo, as I do most of the time. Any suggestions what to show??