Who can tell me about the classic diners?

The "classic" diner didn't differ much from the current ones. A diner was (is) a smaller restaurant, often with a counter as well as tables and/or booths. It was considered the "casual" eating location serving fast meals to the working class citizens in an informal decor and offering a menu of basically home made types of food.

Most restaurants were formal dining areas that enforced "proper dress codes" and offered a menu of dishes that would not usually be prepared in the average home. The average restaurant was visited as a special occasion where the diner (often called a cafe if it didn't have a counter service) served common home style cuisine as an option to carrying their own lunches by workers.

The "sandwich shop" began as a take out version of the diner (and often was a service the diner offered for those who didn't want, or have the time for a sit down meal) and developed into the true "fast food" establishment.

The black and white checkered theme was used by White Castle and Steak and Shake at various times, but I don't remember seeing salted caramel at either. That sounds like something that would be available at a "confection shop", or "ice cream parlor."

The Diner was not the same as A& W or Jack in the Box, Diners were restaurants that were small, and offered a place to sit and eat. Amount the things on the menu were a variety of foods that became part of the fast food menu, but there were also desserts like pie and cake, puddings, as well as full dinners that were offered. Fast Foods were basically burgers joints that offered burgers (not specialized) fires and soft drinks or shakes. The menu was established and changes could not be made. I remember a place that had black and white tile floors, but it was called Harts restaurant and was not a diner or fast food place. I don't remember salted caramel being available at fast food places at all. There was one ice cream shop that made customized stuff and they would do a caramel shake with salt in it. Personally they were no very good.

White Castle restaurants?

Actually neither A&W nor Jack in the box were dinners. Steak and Shake had a black and white color pattern.

mcds