In my paper Realism and Independence I distinguished between modal independence and essential independence.
Modal independence of p from q:
There is a possible world where (p and not q)
Essential independence of p from q:
It's no part of what it is for p to be the case that q be the case
I argued that essential independence from the mental (not modal independence from the mental) is characteristic of mind-independence realism.
But there are other notions of independence in the vicinity as well. For one thing, 'what it is' talk might be interpreted the way I had in mind, as essence talk, or it might be interpreted as more like constitution talk. A third putative notion of independence is
Constitutive independence of p from q:
p's being the case is not constituted by q's being the case.
One reason I don't like the idea of using constitutive independence to characterize realism is that it seems to restrict the range of positions that can be classified as realist. One thing I like about essential independence as defined is that it is supposed to be metaphysically neutral on issues like whether facts or states of affairs exist. (It only talks about 'things being the case', which is intended as lightweight talk that could, but need not, be cashed out in terms of the obtaining of facts or states of affairs.)
By contrast, talk of constitutive independence seems on the face of it not to make sense unless we acknowledge the existence facts or something similar. If we have such things in our ontology, we can perhaps make sense of a constitution relation holding between them, analogous to that which holds between objects (or between objects and stuff).
Are there other ways to make sense of constitutive independence?