chemist's vs chemist's shop

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

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

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

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

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

chemist's (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