family jewels vs private parts

family jewels and private parts both are nouns.

Word	Noun	Adjective	Verb	Adverb
family jewels	Yes	No	No	No
private parts	Yes	No	No	No

As nouns, private parts is a hypernym of family jewels; that is, private parts is a word with a broader meaning than family jewels:

Other hypernyms of family jewels include crotch, genital organ, genitalia, genitals, privates.

family jewels (noun)	private parts (noun)
external male sex organs	external sex organ