drugstore vs chemist's shop

drugstore and chemist's shop both are nouns.

Word	Noun	Adjective	Verb	Adverb
drugstore	Yes	No	No	No
chemist's shop	Yes	No	No	No

As nouns, drugstore and chemist's shop are synonyms defined as:

drugstore and chemist's shop: a retail shop where medicine and other articles are sold

Other synonyms of drugstore include apothecary's shop, chemist's, pharmacy.

drugstore (noun)	chemist's shop (noun)
a retail shop where medicine and other articles are sold	a retail shop where medicine and other articles are sold