Again, as I did yesterday, I borrow from John M. Frame’s concise introductory work to systematic theology. Here he explains the difference subject difference between ontological and economic Trinities.
These are not two Trinities but the same Trinity viewed in different aspects. Of course, since there is only one God, there is only one Trinity. Ontological Trinity is the Trinity in itself, as he exists apart from the creation, as he would have existed if he had never created anything. In the ontological Trinity there is no subordination among the persons, Father, Son and Spirit are equal; that is to say, they are equally God, equally divine.
The economic Trinity, however, is the Trinity in relation to the creation. As we saw earlier, the three persons of the Trinity take on a sort of division of labor with regard to creation and redemption: The Father plans, the Son executes, The Spirit applies. In this great drama the Son voluntarily becomes subordinate to the Father. Jesus says he can do nothing of himself but what he sees the Father do (John 5:19). In John 5:30 he says, “I seek not my own will but the will of him who sent me.” The Father has commanded, the Son obeys. Similarly, the Holy Spirit, when Jesus and the Father send him into the world, “will not speak of his own authority, but whatever he hears, he will speak, and he will declare to you the things that are to come” (John 16:13). See the order? The Father sends; Jesus and the Spirit are sent. The Father speaks of himself; the Son and the Spirit speak the words the Father has given them to speak.
The three persons are equal (ontological), but they take on different jobs (economical) in creation and redemption.