If you feel that “groceries aren't mine until I've paid for them,” then how do you ever eat at a restaurant?
I think a restaurant is different though because that is explicitly how it works (eat first then pay).
To take your comparison further, what would happen if you sat down in a grocery store and started consuming hundreds of dollars worth of food and drink? I think it would raise a lot of eyebrows, and the employees would probably confront you. So there is a difference.
Furthermore, in a restaurant you place an order and they serve you, and from a legal perspective (IANAL) there might be something about some sort of implicit contract that you will pay them. Whereas with a grocery store you are not allowed to remove the items from the store until you've paid for them. And I feel like consuming the items inside of the store is sort of analogous to removing them from the store.