princess vs adult female

princess and adult female both are nouns.

Word	Noun	Adjective	Verb	Adverb
princess	Yes	No	No	No
adult female	Yes	No	No	No

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

princess: a female member of a royal family other than the queen (especially the daughter of a sovereign)
adult female: an adult female person (as opposed to a man)

Other hypernyms of princess include aristocrat, blue blood, patrician, woman.

princess (noun)	adult female (noun)
a female member of a royal family other than the queen (especially the daughter of a sovereign)	an adult female person (as opposed to a man)