Objection 1. It would seem that grace is not fittingly divided into operating and cooperating grace. For grace is an accident, as stated above (Question 110, Article 2). Now no accident can act upon its subject. Therefore no grace can be called operating.
Objection 2. Further, if grace operates anything in us it assuredly brings about justification. But not only grace works this. For Augustine says, on John 14:12, "the works that I do he also shall do," says (Serm. clxix): "He Who created thee without thyself, will not justify thee without thyself." Therefore no grace ought to be called simply operating.
Objection 3. Further, to cooperate seems to pertain to the inferior agent, and not to the principal agent. But grace works in us more than free-will, according to Romans 9:16: "It is not of him that willeth, nor of him that runneth, but of God that sheweth mercy." Therefore no grace ought to be called cooperating.
Objection 4. Further, division ought to rest on opposition. But to operate and to cooperate are not opposed; for one and the same thing can both operate and cooperate. Therefore grace is not fittingly divided into operating and cooperating.
On the contrary, Augustine says (De Gratia et Lib. Arbit. xvii): "God by cooperating with us, perfects what He began by operating in us, since He who perfects by cooperation with such as are willing, beings by operating that they may will." But the operations of God whereby He moves us to good pertain to grace. Therefore grace is fittingly divided into operating and cooperating.
I answer that, As stated above (Question 110, Article 2) grace may be taken in two ways; first, as a Divine help, whereby God moves us to will and to act; secondly, as a habitual gift divinely bestowed on us.
Now in both these ways grace is fittingly divided into operating and cooperating. For the operation of an effect is not attributed to the thing moved but to the mover. Hence in that effect in which our mind is moved and does not move, but in which God is the sole mover, the operation is attributed to God, and it is with reference to this that we speak of "operating grace." But in that effect in which our mind both moves and is moved, the operation is not only attributed to God, but also to the soul; and it is with reference to this that we speak of "cooperating grace." Now there is a double act in us. First, there is the interior act of the will, and with regard to this act the will is a thing moved, and God is the mover; and especially when the will, which hitherto willed evil, begins to will good. And hence, inasmuch as God moves the human mind to this act, we speak of operating grace. But there is another, exterior act; and since it is commanded by the will, as was shown above (Question 17, Article 9) the operation of this act is attributed to the will. And because God assists us in this act, both by strengthening our will interiorly so as to attain to the act, and by granting outwardly the capability of operating, it is with respect to this that we speak of cooperating grace. Hence after the aforesaid words Augustine subjoins: "He operates that we may will; and when we will, He cooperates that we may perfect." And thus if grace is taken for God's gratuitous motion whereby He moves us to meritorious good, it is fittingly divided into operating and cooperating grace.
But if grace is taken for the habitual gift, then again there is a double effect of grace, even as of every other form; the first of which is "being," and the second, "operation"; thus the work of heat is to make its subject hot, and to give heat outwardly. And thus habitual grace, inasmuch as it heals and justifies the soul, or makes it pleasing to God, is called operating grace; but inasmuch as it is the principle of meritorious works, which spring from the free-will, it is called cooperating grace.
Reply to Objection 1. Inasmuch as grace is a certain accidental quality, it does not act upon the soul efficiently, but formally, as whiteness makes a surface white.
Reply to Objection 2. God does not justify us without ourselves, because whilst we are being justified we consent to God's justification [justitiae] by a movement of our free-will. Nevertheless this movement is not the cause of grace, but the effect; hence the whole operation pertains to grace.
Reply to Objection 3. One thing is said to cooperate with another not merely when it is a secondary agent under a principal agent, but when it helps to the end intended. Now man is helped by God to will the good, through the means of operating grace. And hence, the end being already intended, grace cooperates with us.
Reply to Objection 4. Operating and cooperating grace are the same grace; but are distinguished by their different effects, as is plain from what has been said.
Source: Summa Theologica (New Advent)