Im not quite sure and I might be wrong but I think 王女 is a gerneral noun and 姫 is a Honorifics Like さん､さま､くん、and ちゃん　 If you have watched the anime one piece you might of seen the mermaid princessしらほし姫 and her mother is おと姫。and おと姫 is also apart of Japenese mythology she is the daughter of the ruler of the sea the big giant sea dragon watasumi. I don't think Japenese people would say しらほし王女or おと王女. I hope I helped.

And 姫 has more usage. It can be used for part of the name of something small. ex) 姫だこ → a sort of octopus that is smaller than normal type. 姫だけ → a sort of small mushroom

Hello, I'm Japanese (Mulan is just a handle name) so I may be able to help you a little. In the most common use, both of 王女 and 姫 means "princess". But there's a slight of difference. 王女 means "daughter of king", but 姫 means "daughter of somebody noble". Somebody can be Shogun or Lord or else. So, princess Anne from Frozen is 王女 and 姫 at the same time.

Hi, Richard I saw your question title and misunderstood that you were studying Chinese. However some of the Japanese words are original from chinese characters, so I ll just share the chinese meaning of these characters with you, hopefully you ll understand more. "姫" has three meanings in Chinese: a complimentary term for women used in ancient China a title used in ancient China for a concubine a professional female singer "王女" can be seen as"王"+"女", so it means either the daughter of the empror or the woman of the empror.