The immanent Trinity speaks about God in se, God ad intra, God in His being and essence. The economic Trinity focuses on God in His works, God ad extra. The two do not describe two trinities, or two modes of the Trinity, but rather it is a distinction between God's being and God's works. It is foremost the persons of the Trinity who work, and thus, while God is described as working, it is right and proper to talk about the various works of the various persons of the Godhead.
In the immmanent Trinity, the Father is unbegotten, the Son begotten, and the Spirit proceeding. The three are co-equal in all things, without any hint of subordination. In the economic Trinity, the Father is first, the Son submits to the Father, and the Spirit to both the Father and the Son, being sent by both of them. There is an order of submission in the economic Trinity which is absent in the immanent Trinity, but does that imply there is no order whatsoever in the immanent Trinity? What is the relation between the immanent and the economic Trinity?
The two of course speak about the one Triune God, and therefore to say that there is no relation whatsoever between the immanent and the economic Trinity seems to imply different "trinities." God is one, and therefore one cannot separate the immanent from the economic Trinity. At the same time, God in His works is not the same concept as God in His being. How then should we understand the relation between the two concepts (which describe a single reality)?
It is right and Reformed to use the archetypal and ectypal distinction here, and we will. God has archetypal knowledge, and He alone is incomprehensible (which is to say we cannot fully grasp His knowledge even in kind). We only have ectypal knowledge, which is true knowledge true of God and the world, suited for us yet differing from God's archetypal knowledge. The knowledge of God in His being in its fullness belong to God alone in His archetypal knowledge. What we know about God in His being mostly come from philosophizing on how to protect against wrong understandings of God. There is no explicit biblical assertions of the being of God, or even the distinction between being and persons. We are told snippets of facts about God, and through the process of philosophical and theological thought through the history of the church, we have come up with our current Nicene and Chalcedonian orthodoxy.
The knowledge of God in His works however is much clearer, for that shows us how God interacts with us. And here we see there is a certain correlation here between God's being and archetypal knowledge, and God's works and ectypal knowledge. Ectypal knowledge is a reflection of archetypal knowledge, and thus we should see God's works as a reflection of God's being.
We see this reflection at work on a couple of issues. God in His being is a se; God in His works is sovereign and done by Himself alone. God in His being is timeless; God in His works is everlasting. God in His being is impassible; God in His work is constant and faithful in His emotions towards us. God in His being is holy; God in His work sanctifies, and destroys the profane. Whatever is true of God's being is reflected in God's works, not correlated or equated but reflected.
So likewise, in the work of the Pactum we see the eternal submission of the Son. What this is a reflection of is the order of relation in the Trinity. In the being of God, the Father is unbegotten, the Son is begotten, and the Spirit proceeding from the Father and the Son. But here we must note that it is a reflection. The order of submission in God's work is a reflection of the order of relation in God's being, which implies that there is no submission in the order of relation. Eternal generation never implies subordination of any kind, and Nicene and Chalcedonian orthodoxy hold that subordination in the being of God is heresy.
The relation here between the immanent and the economic Trinity is that the order of submission in the economic Trinity is a reflection of the order of relation in the immanent Trinity. I will go further: The terms themselves are explicit reflections of the mission of God. In other words, that we use the term "begotten" and "proceeding" instead of "X" and "Y" to describe the relations between the persons of the Godhead show us how closely the order of relation is to the order of submission. While Father, Son and Spirit are co-equal and none submit to the other, yet the order of relation comes out in the submission of the Son to the Father, and the Spirit to the Father and Son.
The Father is first in order, unbegotten, thus the Father sends. The Son is second in order, begotten, thus the Son is sent. THe Spirit is third in order, proceeding, thus the Spirit is sent by both the Father and the Son. This is the relation between the immanent and the economic Trinity on the issue of His covenantal relationship between the persons, and stands fully in line with Nicene and Chalcedonian orthodoxy as well as the Reformed Confessions.