Coffee shop/coffee house are pretty much the same thing. It's a café-ish type establishment which sells coffee among other beverages. A café is more general, and is generally focused around selling alcoholic drinks. (you can usually still get coffee at these places) A coffee shop in the Netherlands however, is a shop where you can buy weed (marijuana) legally.

I asked my wife to help with this and she had an interesting comment, which I think is correct. In the United States, "coffee house" or "coffeehouse" suggests a place that is likely to have live entertainment on a regular basis. For example, in my home town there is a place that calls itself a "coffeehouse" that has live entertainment Friday and Saturday evenings. The stage is tiny and there entertainment is typically something like a singer with a guitar, or a jazz trio. It has a dozen kinds of gourmet coffee, sandwiches, soups, and salad. In contrast, across the street is a place called the "Bagel and Cuppa," which serves a breakfast menu from 6 a.m. through 1 p.m--pancakes, eggs, waffles. They only have two kinds of coffee: "regular" and "decaf."

多谢！

I (European English) would only use café, never coffeehouse. I didn't realise it was used in the US. I agree with Wik that 'coffee shop' is known all over Europe as a place where you can legally smoke marijuana. It could also be a shop which sells coffee in packets to use at home to make coffee but they don't serve cups of coffee. In marketing they refer to cafés as coffee bars, houses, etc.

In the United States, they are more or less synonyms. There's no absolute rule, and if you want to know what the XYZ Coffee House or the ABC Café is like, you just have to ask someone or go look. "Coffee shop" and "coffee house" are almost synonyms and overlap. However, to me, the word "coffee house" suggests a place that really specializes seriously in coffee, and has gourmet, single-estate coffees and the like. "Coffee shop" is wider and includes casual places like Dunkin' Donuts, where you might go to talk with a friend over coffee and a snack, and the coffee is just ordinary inexpensive coffee--but hopefully freshly brewed. It suggests a local place, perhaps operated by a couple, and senior citizens sitting around reading newspapers and chatting with each other. "Café" is interesting. Although places that are mostly for coffee may have the word "café" in their name, to me the word suggests food, a place with a fairly large lunch menu perhaps. The French word is supposed to suggest a French café or whatever Americans think French café's are like. It might have a lot of tables out in the open air on the sidewalk. I would probably think "food" and not "coffee."