Supermarkets are firms which primarily sell groceries such as:
Kroger, Safeway, SuperValu, Publix, A&P, Albertsons, Whole Foods, etc. The stores you mentioned do sell groceries, but that is not their primary business, and they are not classified as supermarkets for credit card transaction processing purposes.
I'm now even more confused. Some American Express cards (e.g American Express Premier Rewards Gold) have a bonus spending category called "groceries" while others (e.g. American Express Blue Cash) have a bonus spending category called "supermarkets" but based on your answer it seems like that "groceries"="supermarkets".
Why don't just make things simpler and call same things universally? Is that a marketing trick of some kind? Making people think that cards have somewhat different bonus categories when in fact they don't?
Or am I just missing something?