I was reading the wikipedia page about Guy de Lusignan. There it is written that Saladin didn't kill him and said, "A king does not kill a king."
I heard that there were many rules of war during the middle ages, and this made me wonder whether this was one of them, or whether this was a special case.
So, is this an uncommon case, or were kings usually taken as prisoners but never killed by other kings?
A King killing another king was an unwise move for a few reasons. It was a belief commonly held by many nations in the medieval period that kings were anointed by god himself. The belief in the divine right to rule generally extended to kings of other territories as well. Matters of religion and god were far more significant in daily life than in many countries today, and so going against what was seen as god's will (i.e, killing the monarch god appointed) was usually taken quiiiiite seriously. Whether a king himself truly believed that he was divinely ordained does not change the fact that a large majority of his populace likely did. Killing a king was at the very least going to give you a reputation for being unjust but at worst, it begs the question, whats to stop someone else killing you? The idea of divine rule helped to legitimise a monarchs reign, whilst discouraging dissent. It wasn't full proof, naturally, being a king during this era was a dangerous business, so undermining something that might dissuade your murder wasn't exactly in the best interest of a monarchy.
Politically, its likely you're going to shut yourself off from dynasties that would no longer trust a king who would murder another. The damage would hit the economics of a country in terms of trade and definitely leave the country vulnerable if allies turn away from them. There's also the aspect that killing a king is likely to provoke a deadly response from the dead king's successor. Basically, a king would potentially be dealing far more damage to his own realm than that of the one he is removing the figure head of.
More attempted/successful regicide tended to come from usurpers or rebellions than other monarchs as they usually had more motive to (e.g power for themselves or political gain.) Disputes between countries/kingdoms/leaders tended to be solved by treaties (After battles and other drama usually.) England and France are a fruitful example of this, they have a long history of conflict ended with treaties and calm for a while. Henry V actually managed to get himself named heir of France, which shows that power and control could definitely be expanded without having to kill another king.
Some sources on the origins and impact of divine right and regicide in the medieval period
https://www.britannica.com/topic/divine-right-of-kings
https://www.cam.ac.uk/research/news/killing-kings
https://manchesterhistorian.com/2014/the-divine-rights-of-kings/
https://web.cn.edu/kwheeler/Hundred_Years.html (basic overview of the 100s years war between Britain and France which shows almost constant fighting between the two monarchies with essentially no actual impact.)