teahouse vs teashop

teahouse and teashop both are nouns.

Word	Noun	Adjective	Verb	Adverb
teahouse	Yes	No	No	No
teashop	Yes	No	No	No

As nouns, teahouse and teashop are synonyms defined as:

teahouse and teashop: a restaurant where tea and light meals are available

Other synonyms of teahouse include tea parlor, tea parlour, tearoom.

teahouse (noun)	teashop (noun)
a restaurant where tea and light meals are available	a restaurant where tea and light meals are available