For a “naturalist” Nature is “the whole show”. One long string of cause and effect from the big bang forward. There is nothing in “nature” or “the whole show” that self-generates. It’s all just something caused by something else. This goes all the way down to brain function and thought.
Lewis notes that there might be a “sub-nature” of movement of atomic particles which we see as “random” and is perhaps undetermined by the big bang, maybe if you’re a naturalist.
Anyway, a “supernaturalist” believes that “nature” is not the “whole show”. That there are agents who act and move things in nature according to themselves. God is of course such a thing because he caused nature. He is the first cause.
“Naturalists” believe that “the whole show” is all that there is. Everything is a “Group A” sort of thing. If you apply the “spirit of geometry” you can find the math between all things. Complicated all the way down but still just complicated.
Non-naturalists believe that there is another group of things I’m calling “Group B”. These are agents that have a degree of autonomy, freedom from which they act. They are respected often as “persons”. God is of course the source of this Group-B-ness of all other elements of Group B.
Questions revolve around whether Group B exists at all. If not, then naturalism. If so, then the world is not finally subject to the spirit of geometry but we should (as we do) proceed in fear and trembling with the spirit of finesse because, well, God is wild and He creates wilderness. Nature herself is not fully tamed and she too is a part of Group B, even though there is Group-A-ness within her that we employ with power as elements of Group B.