pharmacy vs chemist's shop

pharmacy and chemist's shop both are nouns.

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

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

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

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

pharmacy (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
the art and science of preparing and dispensing drugs and medicines