According To The Teaching of St. Thomas Aquinas
What are we to conclude from all this, save that God is present in all beings and in all places, not as the liquid in the vessel that contains it, since God cannot be contained by creatures, but rather that it is He Who contains them by preserving them; nor as a constituent element of these creatures as the soul is present to the body, for this would be Pantheism; but as the cause and as the active principle is present to the object upon which it exerts an immediate influence. He is present everywhere, not directly and immediately by His substance, although there is no space from which the latter is absent, but rather by His operation and the contact of His power; for the Divine substance being absolute needs no relation with beings existing in time, and being simple and without parts, it, in order to be present any and everywhere, does not have to extend itself through space. Yet since operation, operative power, and substance are not really distinct one from another in God, we must affirm that wherever there is an immediate effect due to the Divine causality, there God is really and substantially present. And as there is not a single creature on which God does not exert His activity to preserve and to move it, it follows that God is present everywhere, not only by His action or power, but also by His essence.
When, therefore, Scripture speaks of God as filling heaven and earth: "Do not I fill heaven and earth, saith the Lord?" these words are not to be taken in their literal meaning any more than the other anthropomorphisms found so plentifully in Holy Writ. God's immensity, as we have often insisted, must not be understood in the sense of extension, and we cannot liken it to a boundless ocean containing in its depths all existing things, interpenetrating each portion of the created world and overflowing on all sides. It is to commentators and to theologians that we must appeal for the true meaning hidden under the expressions the Holy Spirit has employed in order that He might be understood by all. Such was the attitude of St. Thomas toward the above text.
And since being and the other perfections are communicated to creatures in degrees that vary amazingly —from the grain of sand up to that highest of heavenly spirits—the presence of God as efficient cause has also innumerable degrees, according to the measure in which each creature shares in the Divine perfection.