male genital organ vs privates

male genital organ and privates both are nouns.

Word	Noun	Adjective	Verb	Adverb
male genital organ	Yes	No	No	No
privates	Yes	No	No	No

As nouns, privates is a hypernym of male genital organ; that is, privates is a word with a broader meaning than male genital organ:

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

male genital organ (noun)	privates (noun)
external male sex organs	external sex organ