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For all cards that give extra points/miles/whatever at certain types of stores (including the Hilton cards):

The card can't tell what you bought at the store. As long as it's rung up as a "purchase", it'll count, and yes, all those brands count (except I've never heard of Duane Reade, but I'd add Good Neighbor Phramacies).

There might specific items at some stores (maybe some gift cards, and usually lotto tickets) that don't count as purhcases. But in those cases, you probably couldn't purchase them on the same transaction. (In fact, lotto is often cash only to keep it simple.)

And if they don't qualify as purchases, you have a lot bigger problem than not getting bonus points: There are only two options on credit cards, purchases and cash advances, and a cash advance starts charing interest from the moment of purchase.

But you can't mix a purchase and cash advance on one transaction. So, for example, with gifrt cards, if you can buy the gift card on the same transaction as some candy (they don't tell you "well have to run your card separately for this") then if the candy is a purchase so is the gift card.

(It's actual generic MC or generic Visa or generic Amex gift cards that might be an issue sometimes. Branded gift cards -- that you can only redeem with that brand -- are hardly ever an issue.)