In the United States, it is only used to refer to stores that call themselves "bodegas," which are in found in Spanish-speaking parts of many big cities.
In my town, we do not have any "bodegas." We have "convenience stores." That may be a name local to our state and may have something to do with licensing laws for places that sell food.
"Convenience stores" are small stores that sell nonperishable packaged food items--canned, Ramen noodle soup... a refrigerator case with some limited choices of milk, cheese, soda, a freezer case with ice cream and some instant microwave meals. Candy, snack foods, cigarettes. Newspapers, magazines. Lots of lottery tickets, maybe a table in back to play video Keno.