I think Renarin's healing ability is a combination of the two. When he first heals Adolin, he says something like 'He could see a version of himself, except somehow perfected' (I can't remember the exact phrasing, but that's the general gist of it. This leads me to believe that he sees (through Illumination) the spiritual realm-version of the subject (this would explain why the vision appears to be 'better' than the current material person) and then uses progression to make them go closer to it, thus healing them. This could mean Renarin wasn't able to heal Rysn because she had been wounded for so long that it had already made an impression on her spiritual form, like how an object that is broken in the material plane's 'bead' is still whole until you start thinking of it as permanently broken.
