From Christianity today.
You also asked about the roles of all three persons of the Trinity. Here's a brief, though not complete, look:
God the Father's role is to generate things. Things originate with him and flow from him. God the Father is equal with the Son and the Holy Spirit, but things start with him. The Father sent both the Son (John 3:16-17) and Holy Spirit (John 14:26) into the world.
I asked for DIFFERENCES, because you said they were different.
This scripture proves Jesus was involved in the creating of the creation just as the Father was.
John 1:3 Through Him all things were made, and without Him nothing was made that has been made.
Here are more for you:This scripture says all things are from God the Father:
1 Corinthians 8:6 yet for us there is but one God, the Father, from whom all things came and for whom we live;
This scripture says all things are from Jesus:
Romans 11:36 For from him and through him and for him are all things. To him be the glory forever! Amen.
God the Son's role is to pay for our sins with his blood, which he did on the cross (Romans 5:9).
Whose blood is it?
Christ’s blood
1 Peter 1:19
but with the precious blood of Christ, a lamb without blemish or defect.
God the Father’s blood
Acts 20:28 Keep watch over yourselves and all the flock of which the Holy Spirit has made you overseers. Be shepherds of the church of God, which he bought with his own blood.
The Son also acts as a lawyer for us before God, acting as a "mediator" between us and God (1 Timothy 2:5), and speaking "to the Father in our defense" (1 John 2:1).
The scriptures say Jesus makes intercession for us.
Hebrews 7:25 Therefore he is able to save completely those who come to God through him, because he always lives to intercede for them.
The scriptures say the Spirit intercedes for us.
Romans 8:26
In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us through wordless groans.
Romans 8:27
And he who searches our hearts knows the mind of the Spirit, because the Spirit intercedes for God’s people in accordance with the will of God.
Does that prove to you that Jesus is the Spirit?
God the Holy Spirit has many roles. The Spirit helps us pray (Romans 8:26-27).
That scripture is about the Spirit INTERCEDING for us. Please see the scriptures above that show the Holy Spirit does that, and other scriptures say that Jesus does---because none of them are separate and different.
He gives us new life (John 3:3-6).
The Father gives life, John 5:21
Jesus gives life, see 1 Corinthians 15:45 So it is written: The first man Adam became a living being; the last Adam became a life-giving Spirit.
The Spirit gives life; see 2 Corinthians 3:6.
He is our Comforter, and he helps us understand God's word (John 14:26).
The Father is also the Comforter. Jeremiah 8:18
You who are my Comforter in sorrow, my heart is faint within me.
...and the Father gives understanding, Matthew 11:25.
Jesus reveals himself, John 14:21.
...and many more.
He lifts up Christ (John 15:26).
That scriptures says, "When the Advocate comes, whom I will send to you from the Father--the Spirit of truth who goes out from the Father--he will testify about me.”
That says the Spirit of truth.
The Spirit of truth see John 14:16; 15:26; 16:13; 1 John 4:6; 5:6
Jesus is the Truth, see John 14:6; John 1:14, 17.
He convicts us of sin (John 16:7-11).
The scripture is about proving people wrong. Jesus did that too.
He helps us to live holy lives (Romans 15:16).
JESUS SANCTIFIES US
The blood of Jesus sanctifies us Hebrews 2:11; 10:10; 29.
THE HOLY SPIRIT SANCTIFIES US
Romans 15:16 so that the Gentiles might become an offering acceptable to God, sanctified by the Holy Spirit.
He gives us love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control (Galatians 5:22-23)
We have fruit of the Holy Spirit by the Holy Spirit, and the scriptures say by Jesus too, because they are the same.
John 15:5 "I am the vine; you are the branches. If you remain in me and I in you, you will bear much fruit; apart from me you can do nothing.
He helps us share our faith (Acts 1:8).
The Spirit will remind us of what Jesus said. Same, no difference.
And he lives inside us (Romans 8:11).
God the Father lives in believers.
God the Father lives in believers, John 14:23; Romans 8:9; 2 Corinthians 6:16, 1 Corinthians 3:16.
The Spirit of Jesus Christ lives in us.
Ephesians 3:17; Philippians 1:19.
The Holy Spirit lives in us.
The Holy Spirit lives in us, 1 Corinthians 3:16. 2 Timothy 1:14.