I have ambiguity with the meaning of some compound nouns, especially in the form noun+noun like: "The Pirate King", "The Lion King", "The Pirate Bay" and so on.
to put it in context:
Consider this famous movie title: "The Lion King", is it literally another structure of "The King of Lions", meaning are they interchangeable like << the owner of the restaurant = the restaurant owner >>?
Or: "Lion" is a noun but like an adjective describing the kind or type of the "King", meaning literally "the King (of the Jungle) that is a lion"?
If the latter, then doesn’t "The Pirate Bay" mean "the Bay of Pirates"?
Also consider what Luffy said in "One Piece":
I’m Monkey D. Luffy, the man who will become the Pirate King!
With strings of nouns in English it is virtually impossible to deduce the exact meaning purely from grammar, and it usually has to be inferred from context. In terms of pure grammar, both interpretations are possible.
For example most people reading “a pirate king” or “a fairy king” would assume it meant the king of the pirates, or the king of the fairies, but this is based on contextual knowledge that pirates and fairies sometimes have kings over them (at least they do in fiction – and of course the pirate king or the fairy king are normally pirates or fairies).
But for other nouns the reverse would be assumed. A “philosopher king” or a “warrior king” would be assumed to be a philosopher, or a warrior, who was also a king. They would not necessarily be king over other philosophers or warriors. This is again based on contextual expectations that philosophers or warriors don’t usually have their own kings. This could be subverted – for example in a story where philosophers had formed their own nation it might be expected that the philosopher king was king over all philosophers.
If there is danger of confusion you can write “king of the pirates” or “the king who was a pirate”, but if you are reading the phrase on its own you will have to look for contextual clues.