private parts vs crotch

private parts and crotch both are nouns.

Word	Noun	Adjective	Verb	Adverb
private parts	Yes	No	No	No
crotch	Yes	No	No	No

As nouns, private parts and crotch are synonyms defined as:

Other synonyms of private parts include genital organ, genitalia, genitals, privates.

private parts (noun)	crotch (noun)
external sex organ	the angle formed by the inner sides of the legs where they join the human trunk
	external sex organ
	the region of the angle formed by the junction of two branches