Basically, a café is (in the US) a place you go for coffee and other beverages and maybe a light meal, such as a sweet roll or perhaps some pie. However, many cafés will also offer a sort of lunch menu with sandwiches and possibly burgers, fries, etc.
A diner is a place with offers full meals, generally of a relative proletarian nature (versus what would be served in a high-falutin' restaurant). Typically burgers, fries, modest steaks, maybe some fish, a limited selection of salads, and, of course, an assortment of beverages, centered around coffee and soft drinks.
The diner would typically have waiting staff, while the café might be either a server or (stand up) counter service. But either might (or might not) have a sit-down counter, in addition to tables. Typically the café is open for breakfast and lunch only, while the diner is open for lunch and dinner, and maybe open for breakfast, maybe not.
A fast food place would have fare similar to a limited diner, only no waitstaff.
(In fairness--not that New Jersey deserves it--there is a lot of variability across the US as to what these terms mean. My description above is probably most fitting to rural establishments, while metropolitan areas will develop their own quirks as to meaning.)