I understand that and the generic idea that it only matters how a particular store was coded in the application to the payment processing network (AmEx in this case). What I'm pointing out is an apparent inconsistency in marketing between different AmEx cards:

Premier Rewards Gold Card: X2 on groceries, where "groceries" purchases are described as follows "charges at U.S. stand alone ... supermarkets are eligible for bonus points."

Blue Cash Preferred: 6% cash back at supermarkets where "supermarkets" purchases are described as "eligible purchases at supermarkets (excluding superstores and warehouse clubs)"

So at the end of the day X2 on PRG and 6% for Blue Cash Preferred is earned at the exactly same stores even though in one case it's marketed as "groceries" and in other case as "supermarkets". Confusing...