If you let ice cream melt and re-freeze you'll find that it gets very hard. Ice cream is soft because it's frozen foam. Ice cream is churned as it is frozen, and the churning whips the liquid into a foam that has a soft texture when frozen.
On top of that, the churning prevents the formation of large ice crystals which give the grainy texture. Really ice cream is a fatty foam with suspended ice crystals.
Also, if you get it cold enough, It'll freeze plenty hard.
Two different materials ice cream is not frozen water there are fats in it that form different stractures when frozen.
There are sugars and fats in the ice cream that make it require a lower temperature to freeze solid.
The ice cream is churned while it is freezing locking air into it making it lighter and softer.