hard-on vs erection

hard-on and erection both are nouns.

Word	Noun	Adjective	Verb	Adverb
hard-on	Yes	No	No	No
erection	Yes	No	No	No

As nouns, hard-on and erection are synonyms defined as:

hard-on (noun)	erection (noun)
an erect penis	the act of building or putting up
	a structure that has been erected
	an erect penis