A difference can exist, but it does not necessarily have to. It depends very much on how you construct things like God and possibility. To Spinoza, for example, God and nature in the sense you have described may have been effectively identical.
Consider, however, the theist that views God to be a genuinely conscious being with intention and Will. To that person, nature may be the all-encompassing vehicle of that Will, but it will be distinctly not God (or at best, a strict subset of God) because it will be only the dumb manifestation of that will. To analogize, the entirety of a racecar driver's will may be expressed in the form of the action of his or her racecar, but the racecar is distinctly the dumb machine which carries out that will.
Obviously, any actual attempt to separate the two WOULD render them moot--God without Nature is God unexpressed, and Nature without God is Nature unmoved (assuming the construction of the two mentioned above), but one certainly CAN conceptually separate them in this fashion.
Whether or not this has any resemblance to the "true" nature of the relationship between God and Nature is another question entirely, and probably no longer considered fit for philosophical discussion.