Yes, they should, it's network dependent. Usually Visa, MC and Discover have the same MCC, while Amex can have a different one.

I reviewed various Wal Mart transactions done on Chase and even the ones that show as a Supermarket did not get any Chase-Supermarket related bonus back in Q1 on the Freedom card.

I think in the past (years ago) those did get the bonus even though Chase T&C does explicitly state no Supermarket-related bonus on Wal Mart purchases.

I've had multiple locations behave in this manner.

Also forgot to mention if you buy gas at Kroger (Smiths) you need to buy a Smiths/Kroger gift card then use at the pump (scratch off back of gift card for PIN which pump will prompt for). The cash register at the fuel kiosk codes as gas station (just like a gas pump). Kroger/Smiths self checkout will allow gift card purchases up to $500 and after $500 you have to go see customer service (suggest staying under $500).

There is a lot of complexity here. I believe Chase transactions at Wal-Mart go through the private ChaseNet, so it is possible that they get MCC differently, but more often Chase gets a lot of special details to be able to exclude Wal-Mart from 5% grocery bonuses much more easily. I don't know why Chase excludes Wal-Mart categorized as 5% except they don't get enough discount fee to cover the rebates (although they do weird walmart.com only promos, so I just don't know).

I flipped through various in-store transactions at Wal-Mart and they appear to consistently be MCC as supermarkets, but the name/description seems to not be consistent.

Also, Kroger grocery cards appear to have a hard 24 hrs delay. I tried to use a gift card right after purchasing and could not. Thankfully, gas at 5% is more frequent for me than grocery at 5% in rotating categories. The only reason I avoid using direct payment card at pumps is the Albertsons/Safeway side when they do cash/credit pricing and have to get a gift card.