In the US:
“Coffee house” sounds: a bit bohemian, dark, wood, espresso, maybe has
live music sometimes, students and artsy people, most customers at
tables. Servers in street clothes, possibly with an apron; either
queue service or table service. People hang out there. There exist
“Coffee shop” sounds: conservative, brightly lit, formica, Bunn
coffeemaker, Muzak, doughnuts, servers in colored polyester uniforms,
mostly counter service with rotating stools, also a big takeout
business with queue service. A coffee shop is always commercial.
“Café” sounds: more elegant, could be dark or bright, stone, metal,
and wood, but not formica, older crowd, servers in white shirt, black
pants/skirt, apron, counter service (standing, no stools), table
service, terrace service.
Chains like Starbucks and Au Bon Pain I think of as hybrids.
In Europe, things are different. In France and Italy, cafés/caffès are pretty much universally café-bars, and serve coffee, alcoholic beverages, and often breakfast pastries and lunch (usually not dinner).