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Small town in Oregon here (all measured along the routes walked, not 'as the crow flies'):
Now, I'm not entirely sure what separates a supermarket from a "big supermarket" in your mind, because to me all supermarkets are quite big by definition, so I'm going to explore three different trip options: one each to two supermarkets in or near my town, and one to the nearest Walmart, which I'm 100% sure should count as a "big supermarket", but which is a couple towns away.
Supermarket A is close enough that walking to it is a viable option, which would be ~730 meters to the edge of the parking lot or ~875 meters to the front of the store. Alternatively, if I can plan the scheduling of my trip around it or I'm not picky about the timing I can walk ~100 meters to the nearest stop in the city bus loop, wait a while, and walk of right at the front.
Supermarket B is 2.6 kilometers by foot, but a large part of that trip is walking along the side of a lightly-developed highway with no sidewalks, so I don't consider walking here a viable option. By bus it's the same 100 meters to the bus stop, wait, then directly to the storefront.
The nearest Walmart is ~25 kilometers away by car, but the local bus company doesn't offer a direct route to that town so I have to take a bus to Town C, take the Town C Bus Company's bus to the east edge of Town D, then take Town D's bus to the Walmart on the western edge. Google Maps says this would take just over 2 hours one-way, and it would cost $2 ($4 round trip) because Town D's busses are all free to ride at the moment.
In the UK we have smaller "urban supermarkets" that sell everything you might need at home but there's not much choice in it, and there's a lot of ready to eat meal options. Kinda like a corner shop plus.
And then there are the fuck off huge supermarkets that are like THE Wallmart on the interstate on, usually, the edges of urban areas which have foreign food isles, clothes, toys, and more types of toothpaste than you could use in a lifetime of brushing three times a day.