What's the difference between Gran Class, Green Class and Ordinary Glass?

The Gran Class Cars, the pinnacle of luxury in the train system, are an additional improvement over the Shinkansen Green Cars. The Gran Class Cars provide even more luxuries than the Green Cars, including recliner seats that are much more plush and additional leg room.
Alcoholic and non-alcoholic beverages such as sake or apple juice and light meals s are also provided free of charge in Grand Class on some trains (Kagayaki and Hayabusa running between Tokyo and Shin-Aomori).

Note that the Gran Class car is housed in Car 10 of a 10-car Tohoku/Hokkaido Shinkansen train, and Car 12 of a 12-car Hokuriku/Joetsu Shinkansen train.