Trinity doctrine is a quite difficult subject to expound because there is no related existence in the material world.
The important fact is that the Father, and the Son and the Holy Spirit is 'Distinct but not separate.' Therefore tritheism or monotheism is erroneous belief.
The tritheism is believed to have three separate Gods: Father, Son and Holly Spirit. But the Scripture says there is only one God.
However, if we predicate God is one, we tends to see Jesus not as God or God manifests as Jesus as situation require, and such monotheism is also an erroneous belief.
When we think of incarnated Jesus, the distinction between the Father and the Son is relatively clear. And when we consider divinity of Jesus, it's also difficult to understand the distinction because the Word of God is Jesus.
One thing we must remember is that the Father, the Son and the Holy Spirit are always together as One, and never separate.
At the time when Jesus is on earth, it is not that God is in heaven and Jesus on earth in separation. Rather, the Father, the Son and the Holy Spirit are always together as One transcending spaces.
Holy Spirit is Spirit of God, Spirit of Christ, and the Father the Son and the Holy Spirit is always as One.