Tiny stores which typically sell some mix of grocery items, snack foods & (occasionally) prepared food times such as sandwiches, often compensating for a smaller selection and slightly higher prices through the convenience factor of their accessible near-residential locations (aka, the place you go when you just need to run out for some milk or a banana) are called:
@Satsuma i might call it a general store because i think the one that used to exist in my home town had that in the name. i feel like convenience stores in the US do not usually carry grocery items. i am not familiar with either bodegas or corner stores. i think basically i have never actually referred to this type of thing generically. just, like, calling the local one(s) (which other than the one in my home town i feel like i've only encountered in the US on college campuses) by its name/a nickname
@alyssa @Satsuma we live in the town centre and there are 3 supermarkets in walking distance, but wherever we encounter this type of store we call it "alleswinkel" (everything store) because we first went to one in Greece where it's called παντοπωλείο (ditto).