I think it’s easiest to work backwards. Go outside in a dark night where all you can see is the stars. Those stars are illuminated. Thus, By your definition they illuminate the whole world because you can see them and yet no one is going to say that the world at night with no sun up or moon shining is illuminated. It’s dark. It’s not illuminated.
That is it takes more than a tiny amount of light to cause illumination. That is The natural concept of illumination requires something different than the total absence of light.