coffeehouse vs coffee shop

coffeehouse and coffee shop both are nouns.

Word	Noun	Adjective	Verb	Adverb
coffeehouse	Yes	No	No	No
coffee shop	Yes	No	No	No

As nouns, coffeehouse and coffee shop are synonyms defined as:

coffeehouse and coffee shop: a small restaurant where drinks and snacks are sold

Other synonyms of coffeehouse include cafe, coffee bar.

coffeehouse (noun)	coffee shop (noun)
a small restaurant where drinks and snacks are sold	a small restaurant where drinks and snacks are sold