Answer
Oneness doctrine is a rejection of the Trinity and is found in some branches of Pentecostalism. Oneness doctrine teaches that the one God reveals Himself in various forms: sometimes as the Father, sometimes as Jesus, and sometimes as the Holy Spirit. Oneness Pentecostalism, or Jesus-only teaching, is a modern recycling of the old Sabellianism and modalism of ages past.
The classic statement of Trinitarian doctrine is that there is One God who exists eternally in three Persons: Father, Son, and Holy Spirit. The Father is God, the Son is God, and the Holy Spirit is God. However, the Father is neither the Son nor the Holy Spirit. The Son is not the same person as the Father or the Holy Spirit. The Holy Spirit is neither the Father nor the Son. The word Trinity is never used in the Bible, but Trinitarian doctrine is a summary of the teaching about God found in the New Testament.
Oneness advocates resemble Unitarians in that they both deny the Trinity. Unitarians believe in one God who exists as one person, God the Father. The Son is not God but rather a man. Perhaps He was a man who was more fully in tune with God than any other, but a man nonetheless. The Holy Spirit is not thought of as a person but rather as the power of God.
Although the words Oneness and Unitarian would seem to mean the same thing, there is a significant difference theologically. Those who hold to Oneness doctrine believe that the Father, Son, and Holy Spirit are all God. But instead of one God who exists eternally in three Persons, they believe in One God (a single Divine Spirit) who manifests Himself in three Persons or, perhaps more accurately, three personalities. Sometimes the One God interacts with humanity as the Father. Sometimes He interacts with humanity as the Son, and sometimes as the Holy Spirit. This is an ancient heretical teaching called modalism, which taught that God reveals Himself in different modes including Father, Son, and Holy Spirit.
For many who hold to “Oneness doctrine,” Jesus is the primary manifestation of God. Jesus is the Father and the Holy Spirit.
Scripture plainly speaks of one God but also of distinct Persons. These Persons interact with each other. Jesus prays to the Father (John 17 is just one example). If the Father and the Son are not distinct persons, then this prayer is simply a monologue. To whom did Jesus surrender Himself on the cross (Luke 23:46)? And what did John mean when he wrote, “Whoever continues in the teaching has both the Father and the Son” (2 John 1:9)?
While Oneness doctrine would seem to be an improvement over Unitarian doctrine, it still falls short of what the New Testament teaches about the tri-unity of God.