Yes, we do say this in American English. :) A department store is a large store that has several different departments. Each department sells a different kind of product (for example, there may be one department for clothing, another department for jewelry, another for luggage, and another for kitchen items like coffee makers and blenders). A shopping mall is a large area with many different stores. Usually, a shopping mall has a few large department stores and a lot of smaller stores. Some shopping malls are indoors (all the stores, including the large department stores, are inside one huge building, and you stay inside the building when you walk from one store to another). Other shopping malls are outdoors (each store is in a separate building, so you have to go outside to walk from one store to another).

A shopping mall has many department stores inside