There are three major distinctions in God.
First, in the levels: goodness on 3; the Father-Son-Holy Spirit on 2; and simple matter on 1.
Second, between the persons of the Trinity.
Third, between each person's intellect, will, and power.
Regarding the first, just as a human being is a machine-like spirit who features both level 2 and level 1 united into a single creature, so God by His nature consists of all 3 levels.
God's 1st level is almost vacuous: His material cause is simple; and further He is efficiently free. (Thus, God is not composed of any pre-existing material parts, nor operates according to any prior laws of nature.)
God's 2nd-level final cause is His unconstrained enjoyment of perfectly knowing His infinite self.
And God's formal cause -- the answer to the question "What is God?" -- is goodness.
Regarding the second, we can picture the intellect of God as composite and split logically between the persons, such as the Father as "mind or subject knowing," the Holy Spirit as "thought," and the Son as "object known."
His will can be considered similarly: the Father as lover, the Son as the beloved, the Holy Spirit as everything God loves about Himself.
Finally, power: to think (Father), to comprehend with the thought (Holy Spirit), and to be revealed in full, to self-actualize (Son).
Regarding the third:
God's essence as a thinking being is manifested in God's having thoughts. What are the thoughts about? Himself. God comprehends Himself in a single self-image or self-conception.
But comprehending oneself which in this case is holding of one's image in one's mind is owning oneself which pertains to power as possession. (God's power to create the world is due to His 3rd level of goodness.)
Further, since God's happiness lies not in anything outside God but rather within Himself (such that God suffices Himself), for God, again, love of concupiscence is the same as love of self. In keeping Himself in His mind, God ipso facto unites Himself and His understanding of Himself. But love is the only 2nd-level unitive force. Hence, God to His thought is as lover to the beloved. Insofar as God loves the thing He owns, He loves and enjoys Himself.
We can see that the act of God's intellect, the act of His power, and act of His will are one and the same thing, namely, God's conceiving and contemplating Himself. Consequently, the distinction between the three faculties is illusory. God is one (and so is a simple pure act) and supremely so.
Again, God's integrity and fusion of the intellect, will, and power is a separate unity from the unity of the Father, Son, and Holy Spirit. It is precisely my previous conflation of the two that introduced a defect into my system which has now been fixed.