male genitals vs private parts

male genitals and private parts both are nouns.

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

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

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

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