God’s absolute power extends to all logically possible realities. But not even God can create a square-circle (or a stone too heavy for God to lift) because these are verbal unities which do not amount to an ontological unity. The conceptual boundaries of one term (square, for example) exclude or “block out” the conceptual boundaries of another term (circle) and so the combination is contradictory and therefore impossible. To say that God cannot create a square circle is just to say that God cannot create nothing, and that is no knock against God’s being omnipotent, because omnipotence is only concerned with creating things, or at least possible things, which a square-circle is not.
God’s ordained power is related to God’s wisdom (and goodness and justice, etc) and is more what a person should be focusing on when asking “Could God do this or could Go do that?”, if only because when considering God’s ordained power we might reasonably infer not just what God could do but what God would do. Aquinas offers an example of God annihilating the world. This is undoubtedly within God’s absolute power, but it is not within God’s ordained power, because since God has decided to create He now owes it in accord with himself (that is, in accord with his wisdom and goodness and justice) to not blip his creation out of existence willy-nilly. Another example: God could release a demon from hell; that, too, is surely within his absolute power. But it is not within his ordained power. Such a move would not be wise. In short, then, God’s ordained power is whatever God could do that isn’t against his wisdom or goodness or justice. Not just whatever God could do, period (that’s his absolute power).
The notion of God’s ordained power and the restraints or expectations that sets upon God’s action is what follows when understanding that 1) existence is prior to freedom and 2) intellect is prior to will. Nominalists often forget this and that’s why thinkers like Descartes thought God could do such ridiculous things as lie or annihilate himself, which are not only against God’s ordained power, but contradictory and against his absolute power, as well. So, yeah. Big mistake.
God’s ordained power also offers a clue for how to think about the issue of predestination. Is it possible (concerning God’s absolute power) that He move all people infallibly to salvation? Here, I want to say “Yes,” as do many Thomists. But is it wise? Surely not, because we are (as a matter of metaphysical necessity) creatures of fallible liberty, and a wise governor works with all things according to their mode of being, and thus governs fallible creatures in a way that respects their fallibility, which leaves open the possibility of saying no and turning away from God. Of course God does offer every line of help we could possibly need to enter into life with God in heaven, such that if that end is not realized we only have ourselves to blame because of our single unique ability to demerit.
For more see How to Think About God, but also:
We Can Frustrate God’s Uncircumstanced Will But Not His Universal Providence