private parts vs sex organ

private parts and sex organ both are nouns.

Word	Noun	Adjective	Verb	Adverb
private parts	Yes	No	No	No
sex organ	Yes	No	No	No

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

Other hypernyms of private parts include reproductive organ.

private parts (noun)	sex organ (noun)
external sex organ	any organ involved in sexual reproduction