coffee shop vs coffeehouse

coffee shop and coffeehouse both are nouns.

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

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

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

Other synonyms of coffee shop include cafe, coffee bar.

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