princess royal vs princess

princess royal and princess both are nouns.

Word	Noun	Adjective	Verb	Adverb
princess royal	Yes	No	No	No
princess	Yes	No	No	No

As nouns, princess is a hypernym of princess royal; that is, princess is a word with a broader meaning than princess royal:

princess royal: the eldest daughter of a British sovereign
princess: a female member of a royal family other than the queen (especially the daughter of a sovereign)

princess royal (noun)	princess (noun)
the eldest daughter of a British sovereign	a female member of a royal family other than the queen (especially the daughter of a sovereign)