I point to the nicene creed (to make things simpler hopefully to start with) I point to the version which speaks of the holy spirit proceeding from the father (alone):
What is the difference in the nature of how the Son is generated versus how the Holy Spirit is generated? Obviously there needs to be a difference otherwise there would be two Sons which is not in accordance with Church teaching…
…perhaps put in another way, what is the logical precedence in the trinity (Here I mean, that the three persons of the trinity are co-equal and co-eternal in actuality but the father has a logical precedence over the son in the sense that son depends upon being generated by the father. Where does the holy spirit fit into this)?
689 The One whom the Father has sent into our hearts, the Spirit of his Son, is truly God. Consubstantial with the Father and the Son, the Spirit is inseparable from them, in both the inner life of the Trinity and his gift of love for the world. In adoring the Holy Trinity, life-giving, consubstantial, and indivisible, the Church’s faith also professes the distinction of persons. When the Father sends his Word, he always sends his Breath. In their joint mission, the Son and the Holy Spirit are distinct but inseparable. To be sure, it is Christ who is seen, the visible image of the invisible God, but it is the Spirit who reveals him.
The Holy Spirit has been described as the (for lack of a better word) byproduct of the Father and Son’s mutual love for each other.
You must understand Noorez that in Christianity that the Catholic Church has her version about the Trinity and the Eastern Churches have their version about the Trinity. Surprisingly the two Churches do not agree on the Holy Spirit. I suspect though they think both are right and if you check their interpretation it is right depending on how they define the Holy Spirit accordingly to what they believe. I often believe that the Holy Trinity can be simply explained by using the best model we have which is the family. The Holy Trinity had created the human race by the best example which God knows and that is Himself. Within the Godhead is a family of three persons, Father, Son and Holy Spirit. Since God is a family of three Divine persons He created the human race after the only model which is known by Him. Every family on earth is kind of a mini trinity. The Holy Family of Jesus, Mary and Joseph is a representation of the Holy Trinity. Every father in a family represents the Eternal Father, every child represents the Son of God and every mother represents the Holy Spirit. God designed the human race as a reflection of Himself.
What goes on within the Trinitarian God is a great mystery. Jesus explains the eternal procession of the Holy Spirit as coming only from the Father. I believe Jesus had spoken the truth. What He means by proceeding is something we cannot fathom or understand. The Son being begotten of Father in eternity is something else we cannot understand. We take it by faith what was written is the best possible definition we can put forward even though the words really do not signify any understanding on our part. For us to fully understand these statements we have to be God and since we are not God we have only words that poorly give to us these definitions. Only God can know Himself perfectly. Yet if we want to understand some of the majesty of the Lord we can look to the family for it is within the framework of the family that God had decided to design His best work. As I said earlier God had no blueprint to create us except for who He is. Since the Holy Trinity is expressed as a family of three Divine Persons it was natural for God to create us after the only model He already enjoy.
God created man and woman in God’s image and likeness. Man breathes and speaks.
When God speaks and breathes from His Essence Existing eternally (metaphorically speaking here)
The distinction is revealed in the Voice that is heard from God the Father, what proceeds within and from that voice is God the Son who is the Word of God proceeding, generating revelation of God’s presence. What proceeds from God’s Voice, distinctly from God’s Word is God’s Breath =God the Holy Spirit who proceeds from both the Voice and the Word in presence to make known the revelation of God from God’s presence.
Does this explain the Trinity, NO, not even close. It is just a reflection of What God has revealed to our humanity with God’s presence in space and time =human history.
The Trinity is never divided because the voice, the word, the breath are all one God in being. Yet each one is distinct in revelation of the other, the voice is God, the word is God, the breath is God. They are distinct in procession, generation, revelation of God’s presence, never divided, not separated or confused One God in Essence being.
Things to consider; The Son eternally proceeds from the Father is a mystery that relates to God’s Essence being Existence itself which eternity obeys and space and time cannot comprehend.
Thus God’s Essence is not revealed in space and time, but God’s presence is revealed in space and time with God’s presence in the Father (voice), the Son (Word) and the Holy Spirit (breathe), when all three are distinct in presence , all three distinct persons is God’s Essence being, for the presence of God proceeds in Trinity to our humanity. While God’s presence veils God’s Essence. When no one can see God and live. But scripture reveals only the Son has seen the Father because the Son comes from the Father and the Father and the Son is one, this is spoken of an eternal relationship with the Holy Spirit proceeding from both in Trinity, Life breathes life eternally to give life to our humanity, when we profess God from God, Light from Light.
Eternal procession, presence, substance=Essence= divinity, eternal begetting, eternally begotten, sending and proceeding, generating are terms that point to God’s presence existing in eternity being made present in space and time. God has revealed this throughout human history recorded, God reveals His presence in space and time in Trinity, the voice, word and breath of God reveal persons living and being God, the Father, God the Son and God the Holy Spirit.
Yes. The Son can be thought of as generated from the operation of the divine intellect–the Father knowing himself so perfectly that his idea of himself–the Divine Word–is perfect, not even lacking personhood. The Spirit can be thought of as generated from the operation of the divine will–the Father and Son’s mutual love generating a third person, the Holy Spirit.
The nature of all three persons, of course is exactly the same–the one divine nature.