male genitalia vs private parts

male genitalia and private parts both are nouns.

Word	Noun	Adjective	Verb	Adverb
male genitalia	Yes	No	No	No
private parts	Yes	No	No	No

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

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

male genitalia (noun)	private parts (noun)
external male sex organs	external sex organ