I think "go/do shopping" is the same in French, Spanish, Italian and German, as opposed to faire les courses / ir de compras / fare la spesa / einkaufen.
In US english (at least as I speak/understand it) "shopping" is any act of browsing/looking at/selecting something for purchase. It can be groceries, clothes, a car, anything really and it can be online or in person at a store.
"I'm going shopping" with no other specifics would normally mean "for groceries" or other general household supplies, though.
"walking the strip and dreaming of buying random clothing" is "window shopping"