Matt 26: 39 And He went a little further, and fell on His face, and prayed, saying, O my Father, if it be possible, let this cup pass from me; nevertheless, not as I will, but as thou wilt. John 6: 38 For I came down from heaven, not to do mine own will but the will of Him that sent me. From these verses we can see that the Father and the Son have different wills although the Son subjugates His will and obeys the Father's will. Christ is the God who is active in both the Old and New Testament and fulfills the Father's will.
Exodus 6: 3 And I appeared unto Abraham, unto Isaac, and unto Jacob, by the name of God Almighty, but by my name JEHOVAH was I not known to them. Christ appeared to them in the name of the Father but His name is Jehovah. It was the Father that appeared in Spirit because Christ is filled with the Father's Spirit and and the Father's Spirit talks through Christ ( JEHOVAH) (who is also a spirit).
Christ is our Savior, our Lord, and our God, but the Father is the father and God of all. Christ died for all mankind and wishes that all be saved but the Father's justice demands that only a few be saved. If He saves all, there is no justice because we are all condemned already and sin would have to be allowed in heaven which means that He would no longer be sovereign. If He condemns all, He would be merciless. To show His mercy, He saves a few by baptizing them in His name by bestowing on them the state of being of repentance for their sins so that the sinner turns to Him for forgiveness.The Father in turn uses different means to bring him the knowledge of forgiveness of sins through Christ. Christ then baptizes the repentant sinner in His name by bestowing on him the faith needed to believe in His work on the cross for the forgiveness of his sins and in the name of the Holy Spirit when the cleansed but still sinful sinner gets perfected. He gets filled with the Spiritual essence of the Father and the Son who fill his heart with the divine love necessary to obey the Spirit of the Law given by Christ which is to love God first and everyone else as he loves himself.