Question: The term is [妖精](https://zh.wikipedia.org/wiki/%E5%A6%96%E7%B2%BE), which can be translated into English as "fairy", "elf", "goblin". As noted, the Japanese literature uses 妖精 to describe the European fairy. The English translation of 白骨精 in 西游记 (Journey to the West) is "white bone demon". So, this word can be translated into English as fairy, elf, goblin, or demon. 

Let's say an author is writing a fantasy story in Chinese first, using terms that are understood in a Chinese society. Then, the same author translates his/her own story into English and faces a problem. Which term should 妖精 be translated into (fairy, elf, goblin, or demon)? Or are the differences between the terms negligible, so the author can just pick a random one and go with it?

Answer: 
In your example, 白骨精, I'd say the 精 is not so much 'fairy' as it is in 妖精, but rather 'spirit' (like in 精霊), similar to how in English we can use the word 'spirit' to describe a lot of different types of ghouls and ghosts, so spirit might be a good choice as a kind of 'all round' title. 

Anyway, I don't have a definite answer, but I would say there's two options.

Option one, rather than translating the other language into an English equivalent you could simply use the foreign word. For example, a 僵尸 would simply be 'jiangshi', rather than 'Chinese hopping vampire'. This would work best if what you're writing is set in a world or country that comes across as foreign to English readers anyway, whether you use English to describe the creatures or not. After all, most people are unfamiliar with foreign mythical creatures, so in some cases the English may give no more of an idea of what the creature is like than the original foreign word. 

But then for option two (which is the one I'd use), to be honest I would just say to choose which word (ghoul, fairy, spirit, demon) fits with the image of the creature. Is it small and cute and not very mean? Fairy or spirit should do. Is it ugly and bad, but maybe not so deadly to humans? Maybe ghoul would work. Evil and malevolent and otherwise hurts people? Demon or devil it is.

When it comes to writing the author has a lot of leeway with naming and making up creatures, so I would go with whatever you feel fits the best, whether that be the English or the original word.
I suspect you may be missing one - the Aos Sí (or Sidhe) from Irish mythology. They are the 'fair folk' or the 'lordly ones'. They can be beautiful and hideous. They predict/cause death. They are relatively benign, unless angered. They fit all of fairy, elf and demon. 

One Sidhe would give artists and musicians their inspiration - at the cost of their life. Others would steal children. 

Modern (IE Tolkien/D&D) elves derive from this as does fairies, banshees, leprechauns and others. Over time these usages have become biased towards cartoonish niceness. 

I'ld go for White Bone Demon or White Bone Elf depending on how potentially evil they are. 

(would post this as a comment, rather than an answer)