tobacco shop vs tobacconist shop

tobacco shop and tobacconist shop both are nouns.

Word	Noun	Adjective	Verb	Adverb
tobacco shop	Yes	No	No	No
tobacconist shop	Yes	No	No	No

As nouns, tobacco shop and tobacconist shop are synonyms defined as:

tobacco shop and tobacconist shop: a shop that sells pipes and pipe tobacco and cigars and cigarettes

Other synonyms of tobacco shop include tobacconist.

tobacco shop (noun)	tobacconist shop (noun)
a shop that sells pipes and pipe tobacco and cigars and cigarettes	a shop that sells pipes and pipe tobacco and cigars and cigarettes