by-product vs event

by-product and event both are nouns.

Word	Noun	Adjective	Verb	Adverb
by-product	Yes	No	No	No
event	Yes	No	No	No

As nouns, event is a hypernym of by-product; that is, event is a word with a broader meaning than by-product:

Other hypernyms of by-product include consequence, effect, issue, outcome, result, upshot.

by-product (noun)	event (noun)
a product made during the manufacture of something else	something that happens at a given place and time
a secondary and sometimes unexpected consequence	a phenomenon located at a single point in space-time; the fundamental observational entity in relativity theory
	a phenomenon that follows and is caused by some previous phenomenon
	a special set of circumstances