There is no real difference. A "store" tends to be larger and to sell a variety of things. A "shop" tends to be smaller and sell only one kind of thing. In the United States nowadays I would say that the word "shop" is not used often any more because there are fewer and fewer small stores. It's safer to use the word "store," because it is OK to call a little shop "a store," but it sounds strange to call a huge store "a shop." The word survives in the _verb_ "to shop." We would actually "I like to shop in the mall because it has so many stores."

I believe shops are typically smaller then the average store, that would probably be the only difference.