chemist's shop vs apothecary's shop

chemist's shop and apothecary's shop both are nouns.

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

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

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

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

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