[mesmark]

cafe and coffee shop are the same, as far as I know. cafe sounds a bit more posh.

A cafeteria is different. A caferteria has a food counter and is usually a line of food that the customer moves along and then selects what they want. This differs from a buffet in that the customer has to pay individually for each item they select (or there may be a limit to what they can select and how many, as with school cafeterias.) There's generally a large area for sitting and customers seat themselves.

I don't know of any differences between American and British usage. (I'm American, btw.)