C. Matthew McMahon's book The Two Wills of God has three main points, and I will go through one point per post.
There are three questions here: One, are there two wills of God? McMahon's answer to that question is no, but the one will of God has two senses, the compound sense and the divided sense. Two, is there a sincere offer to all men of God desiring their salvation? McMahon's answer is God sincerely desires the salvation of all in the divided sense, but not in the compound sense. Three, is there common grace, defined as a disposition in God towards the well-being of the reprobate? McMahon's answer is no, but there is indiscriminate providence towards both the elect and reprobate.
Compound and Divided Senses
So what exactly are the compound and divided senses? The compound sense is "God's interpretation of His own being given to us in the condescended language of the Bible" (p. 507), while the divided sense is "the revelation of God in the realm where perspective of man would be used" (p. 74), or "the human view of God seen through the historical narrative and written letters of the Bible" (p. 507). The descriptions of these senses more closely match the divine and human perspectives, as revealed for us, respectively. These two senses, since they operate on different planes, are not contradictory, functioning like pieces on two different boards of chess (p. 77). If however, one were to collapse the two senses into each other, one would operate with a very crowded "board" and justice would not be done to all the truths of Scripture. In this light, the PRCA (Protestant Reformed Churches of America) according to McMahon would not escape the charge of Hyper-Calvinism because they fail to differentiate the two senses (p. 82). Likewise, the primary opponents of McMahon's thesis, the sub-Reformed teaching concerning the two wills of God, "common grace" and the well-meant offer of effectual grace, are guilty of the same failure to do justice to the full teaching of Scripture.
How should we think of McMahon's differentiation of the compound and divided senses? The terms are coined by him of course, but the concepts seem to be helpful. We most certainly must hold to God's simplicity so God cannot have two wills, and the division between the compound and divided senses help us to preserve the one will and also to note how God's will is expressed differently, which traditionally is stated as the difference between the preceptive and the decretive wills. What is traditionally known as the "preceptive will" can be thus expressed as the divided sense of God's will while the "decretive will" as the compound sense of God's will.
Aside from the heuristic benefits in differentiating the two senses, the terms themselves ("compound" and "divided") are rather cumbersome. While helpful, I do not believe they go far enough in showing us in what manner the compound sense convey God's interpretation relayed to us, and in what manner the divided sense convey the human view as shown by God. The technical fine line will certainly be lost to most people. To this, I think that bringing in the notion of corporate or federal identity would be more helpful. Instead of leaving it as the compound sense, why not we understand that as the sense towards individuals, towards particular individuals? Instead of leaving as the divided sense, why not we understand it as towards the collective, as an expression of God's principles?
The compound sense speaks about God's interpretation, and thus its locality is in God's intention and desire. It is analogous to the decretive will, which is what God desires and enacts and decrees. It is thus what God will do to individuals, in particular election and reprobation. It seems that the three can be placed side by side as analogous ways of looking at God's will as what God desires: Compound sense - Decretive (Sovereign) - Particular.
The divided sense speaks about the human view, and thus its locality is in God's commands showing forth His nature. It is analogous to the preceptive will, which is what should be done to be congruent with God's ethical nature. It is thus also what God would see as being perfective for all corporately, in covenant solidarity. Side by side the three are to be seen as analogous ways of looking at God's will as flowing from what is perfect: Divided sense - Preceptive - Collective (Federal).
For simplification, we can say that God wills something for the whole (collective) that is realized for the part (Particular). This I think is a good and biblical and simpler way of understanding the compound and divided sense, from another point of view.