I live in a suburb with few shops and cafes but next to a suburb with shitloads of them so I consider the neighbouring suburb as local. Its about a 25 minute walk I reckon.
Although if someone referenced the “cornershop” I wouldn’t expect it to be anymore than a 5 minute walk.
So the answer is, if it’s got corner in the title it has to be super local, otherwise anything less than 25 minutes walk.