Undeleted my answer, though it's incomplete. I'm aware that even with root access, there are certain things a rooted app can't do. Elixir 2, for example has a System add-on which allows the GPS toggle to turn on GPS directly through its widget. Without this, the GPS toggle opens the screen for you to turn on the GPS manually. Maybe someone else can explain.
An app is either a user app or a system app. A user app is stored in the
/data folder, while a system app is stored in the
/system folder. To access either folder, you need root access.
Giving a user app root access means it can perform actions that requires root access, such as accessing / modifying system files.
But what makes a system app unique is that it doesn't get deleted if you do a
Factory Reset. It becomes part of the Android Operating System.