You have to realize that the ice cream is a specific type of frozen dessert. The ice cream usually needs to be placed in the freezer so that it can maintain its cream form. The creamier the ice cream is, the softer that it will remain even if it has been placed in the freezer for a long time. When you say frozen dessert, this can mean different things.
There are other frozen desserts that are available. There are some cakes that are required to be frozen so that they will be able to maintain its shape. Take note that there are a lot of frozen desserts that are made with a certain type of oil, usually vegetable oil so that it will be able to freeze properly.