Shopping was actually surpringly not different from shopping in the US. I never got a bank account in Scotland, because I could do everything by Visa or an ATM card. (And used cash for the places that couldn't take Visa, generally.)
Once inside the stores, one Safeway is like another Safeway. But the names have been changed. Hand Dishwashing soap is now Washing Up Liquid. Potato Chips are now Crisps. Cookies are biscuits. And so on. Nearly everything we wanted was here, but we just had to figure out what it was called! ("Is washing up liquid for dishes or for clothes?") The next problem after product identification is deciding where to go to buy something. Where do you buy sheets? Good question. That's before you realize that Next isn't a computer, and M&S isn't a weird relative of M&Ms, and it all gets worked out.
After settling in, and pretty much exhausting the excitement of the good ol' grocery store, there is plenty to discover in the "real" stores - the butcher, the cheese shop, the bakers, and so on. The butcher was not only helpful and all that, but they delivered on account, for free! I've never seen service like that in the US, ever. Bread was best bought from the baker, and the selection of cheese was just astouding (as was the smell) from the local cheese shop.
As long a stuck to the small local shops, the people in the shops were really nice, friendly, and service oriented. The larger the place, the more disorganized, unhelpful, and all that they were, just like American Giant Chain Stores.