The definitions for both are very loose and vary depending on the region where you live.  Generally speaking, tomato soup is usually made with chicken broth, chicken stock or vegetable broth, even though it might still have some heavy whipping cream.  A tomato bisque recipe has a greater use of heavy cream and is often what you will get at a restaurant if you order a classic tomato soup recipe or tomato bisque soup recipe.  It's definitely more of a common term.