The Scripture does make a clear distinction between God the Father and the Holy Spirit.

The Father Sent The Holy Spirit

The Bible says that God the Father sent the Holy Spirit. Jesus said.

But the Helper, the Holy Spirit, whom the Father will send in my name, he will teach you all things, and bring to your remembrance all that I said to you (John 14:26).

The Father will send the Holy Spirit, not Himself, to help believers.

There Is A Difference Between The Father And The Holy Spirit

The Holy Spirit does the will of God the Father. Paul wrote.

And He who searches our hearts knows the mind of the Spirit, because the Spirit intercedes for the saints in accordance with God’s will (Romans 8:27).

Summary

The Bible makes a distinction between the Holy Spirit and the Father. The Father sent the Holy Spirit into the world – the Holy Spirit did not send himself. In addition, the Holy Spirit does the will of the Father – not his own will. Clearly they are not the same Person.