They do serve the same purpose. UM and UIM replace the injury coverage that the at-fault party doesn't have at all (UM), or doesn't have enough of (UIM).
Lots of states require that you purchase UM. In the states where UM and UIM are not separated, that means you're paying for both whether you want to or not. In the states that do separate them but also require UM, it allows people to reduce their costs by choosing not to have UIM if they don't want it. Those are the states that I listed.
Looks like you need to add Illinois to your list.
