But in AE at least it isn't the same thing as a cafeteria and isn't, I am pretty sure, short for it. It means a relatively small and informal restaurant that, presumably serves coffee. I am virtually certain it comes from the French café (hence the accent) and has pretty much the same meaning (though whether the coffee will be as good...?)
At least in NA they are quite different. A cafeteria is marked by self-service. You take your tray along the line and take or are given food and drink. It would not be entirely illogical to say "a cafeteria style cafe/coffee shop" (though how that would differ from just a cafeteria isn't clear).
In NA cafe and coffee shop are pretty much synonymous.
In NA this really doesn't ring true. Most cafes just serve coffee (one sort, plus, maybe, decaf for wusses). If you were to ask what sorts of coffee they sell, you would be directed to the Starbucks down the street (for which the term cafe would probably not be applied, interestingly MS Word just automatically added the accent to cafe).
On the other hand, there's the Hard Rock Cafe (without an accent).
In AE a cafeteria is usually a large, brightly-lit room where people stand in line with a tray, moving food to the tray as they pass various offerings. At the end of the line, they pay a cashier for the food on their tray. They then eat the food, usually at communal tables. Cafeterias are associated with institutions such as schools, or organizations such as corporations.
