God is a Trinity, Father, Son, and Holy Spirit. The three persons are one and the same. The Son is emanated from the Father, and the Holy Spirit is emanated from the Father and the Son. However, they are only one God. They are produced in no particular order and transcend time and space.
Gabriel is just a messenger who conveys God's will. Without the inspiration of the Holy Spirit, Saint Mary would not have obeyed her will.