1: Physical: Users can erase anything on a physical level, reducing the item or person to absolutely nothing.
2: Non-Physical: Users can not only erase anything physical but also anything incorporeal, destroying the item or person on the Spiritual and or Mental levels, leaving no traces of them behind.
3: Space-Time: Users can erase things, not only on a physical and spiritual level, but across Space and Time itself, leaving no traces of them across Time and Space, possibly changing history to suit the change.
4: Conceptual: Users can erase concepts and the fundamental aspects of one's existence, removing the very idea of their existence from reality, meaning they never did exist, never will exist and cannot exist on a conceptual level. Users can even erase one from the narrative itself, leaving nothing of them on a narrative level. It should be noted both of these are interchangeable.
It should just be like this. To qualify for space-time erasure you must also erase that being on a physical and spiritual level.
This from debates jungle btw.