multiple vs product

multiple and product both are nouns.

Word	Noun	Adjective	Verb	Adverb
multiple	Yes	Yes	No	No
product	Yes	No	No	No

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

Other hypernyms of multiple include mathematical product.

multiple (noun)	product (noun)
the product of a quantity by an integer	an artifact that has been created by someone or some process
	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

multiple (adjective)	product (adjective)
having or involving or consisting of more than one part or entity or individual