by-product vs product

by-product and product both are nouns.

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

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

Other hypernyms of by-product include production.

by-product (noun)	product (noun)
a product made during the manufacture of something else	an artifact that has been created by someone or some process
a secondary and sometimes unexpected consequence	items for sale to the individual consumer
	a quantity obtained by multiplication
	the set of elements common to two or more sets
	a consequence of someone's efforts or of a particular set of circumstances
	a chemical substance formed as a result of a chemical reaction