Nobody knows what the substance of God is. He exists outside our universe of time, space, and matter. Or rather, our universe exists somewhere in God. He gave the energy and wisdom that brought the universe into existence 13 billion years ago.
Angels are spirits, but they are still part of our universe. In that sense, their substance is still defined in terms of the “substances” of this universe. Perhaps their substances are energy waves or magnetic fields. Who knows? We will know one day. But my point is that the substance of God is completely different from even the spirit substance of the angels.
The Bible says nothing about the substance of God, except perhaps Hebrews 1:3, which says that the Son is "the exact representation of" God's substance. But it seems as if Arius and his supporters, in the time before Nicaea (325), argued that the Son is of a different substance than the Father for the creed condemns all people that say that “the Son of God is of a different hypostasis or substance” (than the Father). In other words, Arius and his crowd argued for a substantive difference between the Father and the Son (pun intended).
The creed responded that they are homooúsios, meaning “same substance” (from the Greek words homos, same, and ousia, essence). (Merriam-Webster)
After the Nicene Creed was formulated in 325, the church reacted strongly against the word homooúsios and developed many creeds to replace the Nicene Creed and, in particular, the word homooúsios. These views include the following:
DISSIMILAR SUBSTANCE - Heteroousianism held that God the Father and the Son were different in
substance and/or attributes. These were called the extreme Arians.
They described the Son as "unlike" (anomoios) the Father.
(Encyclopedia Britannica, 1979, Arianism, Vol. I, p.509) For example, Emperor Constantius (Constantine's son) requested a council at Constantinople in 359 where the Heteroousians (dissimilar substance) defeated the Homoiousians (similar substance) in an initial debate. (See council of Arinimum.)
SIMILAR SUBSTANCE - Homoiousianism (from hómoios, "similar", as opposed to homós, "same,
common") maintained that the Son was "like in substance." They
were called Semi-Arians.
NO SUBSTANCE - Homoeanism declared that the Son was similar to God
without reference to substance or essence. They held that the Father
was like the Son in some sense but that even to speak of ousia was
impertinent speculation. Hanson, RPC, The Search for the Christian Doctrine of God: The Arian Controversy 318-381 AD, lists twelve creeds
that reflect the Homoian faith.
ONE SUBSTANCE - However, later in the fourth century, spearheaded by the Cappadocian fathers, the concept developed that the Son is not
only of the “same substance” as the Father but also “one substance”
with the Father. This later became the standard Trinitarian
formulation. While all the other views held that the substances of the
Father and Son are distinct, even though they may be the "same
substance" (same type of substance), just as your and my substance is the same but distinct,
the “one substance” view proposes that they ‘share” one single
Note that the Nicene Creed of 325 is not Trinitarian in the sense of three Persons but one single substance. That concept was developed later. The emphasis of the Nicene Creed was merely the equality of the Father and the Son.
In Reformed circles, where I grew up, the “one substance” view is often expressed by saying that God is three Persons but one Being.
You ask: How are the Son and the Father different? You added: We cannot say that Jesus is God in the sense of identity. The different views above will give different answers. But the orthodox answer, as expressed by the Athanasian Creed, is that they differ only with respect to relations, namely:
- That the Father begets the Son and
- That the Holy Spirit proceeds from the Father and the Son (in Western orthodox theology).
But if they share one single substance and one single mind, as per the orthodox understanding of the Trinity, what is the practical difference between the three Persons? This is addressed in the question about Modalism.