Question: I've read terms like ontological subordination and economic subordination. If the early churches taught that Jesus is subordinate to the Father, which of these do they mean?
You're ahead of me theologically, it appears. I've never heard those terms, though I can guess what they mean.
Ontological subordination must mean that the Son is subordinate to the Father in his very being. He is somehow not as great as the Father and never has been.
Economic subordination must mean that the Son is only subordinate to the Father is a special "economy," or system of things. That would be a reference to his time on earth, when he was in a body. Most Christians, I suspect, would have no problems with economic subordination. After all, Jesus not only said that the Father was greater than he was (Jn. 14:28), but he also said that not even he knew the day and time of the end. The Father has reserved that knowledge to himself (Mk. 13:32).
The early Christians definitely teach economic subordination, and they would also teach at least some form of ontological subordination. I'm just going to describe their teaching here, and you can go to "Are God and the Word Equal?" for the quotes and references.
The early Christians describe the Word (Jn. 1:1) as equal to God in the sense that he shares the same essence.
The early Christians referred to the material God used to create everything, including living beings, as matter. Matter, because it once did not exist, is inherently temporary. It is not eternal, at least not in and of itself. Nothing that once did not exist can be eternal.
The Son of God was not created. He was birthed or generated from inside God before the beginning in a manner that we can never comprehend. Unlike matter, he has always existed. He is the Logos of God, which in English can be translated as Word, Message, or Reason of God. The early Christians understood this quite literally. Somehow, God was able to generate his Word/Reason from out of himself so that God, quite literally, has a Son.
The Son is equal to the Father in that he shares the "essence" or "substance" of God. Because God is infinite, then his essence fills all things. It cannot be divided. Thus, even though God has a Son, they share the same "essence." The Son is equal to the Father because he, too, is of the indivisible divine substance. This is why the Nicene Creed was formulated with the words "begotten, not made, one in substance with the Father."
This one's easy. All of us know that the Father sends the Son, not vice versa. Even before Jesus was on the earth, according to Jesus himself, "God so loved the world that he sent his only-begotten Son" (Jn. 3:16).
This also explains a very bizarre passage in Zechariah. In the second chapter of the prophet Zechariah, we read about "the LORD of hosts" saying that "the LORD of hosts sent me" (vv. 8-11). This is obviously the Father sending the Son even before he came to this world as Jesus of Nazareth.
The early churches, just like most of us do, believed Jesus was subordinate in position, always doing the will of the Father.
We have already seen that the early Christians considered the Father and the Son equal in essence:
You will see, however, in the following description that they did not consider them equal in all ways. This, I suppose, would be referred to as ontological subordination.
The early Christians believed that every appearance of God in the Hebrew Scriptures was actually an appearance of the Son of God. There are several compelling scriptural reasons for believing this, but the explanation given by the early Christians was that God, being God and filling all things, could never be confined to a place. In fact, because he fills the universe, he can never be seen.
The Scripture agrees with this, telling us in John 1:18 that no one except the only-begotten Son, the Word, has ever seen God.
You will also find early Christians, in so many words, saying, "Of course the Father is greater than the Son because God is greater than his Word." For example:
So, to the early Christians, Jesus was saying that the Father was greater than he was both while on this earth and even throughout his pre-existence.
Again, for more quotes, and a longer discussion of this issue, go to "Are God and the Word Equal?".
I have a large number of quotes on the whole issue of the Trinity, rather than just subordination, in Trinity Quotes.
I have written an entire book on the Council of Nicea that addresses the topic of the Trinity from the early Christian perspective as thoroughly as you will ever find it addressed. You can read the two chapters that directly address the issue of the Trinity, or you can get the book that tells the whole story of the Council of Nicea and why they made the decisions they did.