A food store is a store where you buy food. The primary purpose of your visit is purchasing food, not "grocery" items. A food store often sells "grocery" items, but you don't buy them because they're cheaper at Wal Mart. Often, people mistakenly refer to the food store as a "grocery store," but never buy any "groceries."
I went food shopping at food store this weekend. I did not buy any grocery items at the food store because they're cheaper at Wal Mart.