Department Store - A large store divided by departments, each specializing in a different product. shoes, apparel, sports, ect.
Conveniance Store - A small store that sells small personal sized items such as candy, newspapers, coffee, and similar items meant for quick use. For your conveniance.
Shopping Mall - Is a collection of different stores under one roof.
Supermarket (one word) - Is a larger type of conveniance store, but the items it sells are meant for later use. It generally sells food plus items used in the home. By later use I mean it is for stocking your house, your fridge, medicine cabinet, ect rather than for immediate use (conveniance store).