There is an ancient heresy that assumed that the Holy Spirit was not a distinct person from Jesus but rather another name for Him. This is known as Binitarianism. This teaching is found in an early work known as The Shepherd of Hermas as well as the Macedonian heresy of the fourth century.
The belief is derived from statements that seem to link the two together. For example, Paul wrote to the Romans
You, however, are controlled not by the sinful nature but by the Spirit, if the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, he does not belong to Christ (Romans 8:9).
It is argued that the spirit of Christ is Christ Himself. Thus the Holy Spirit is just another name for the Spirit of Christ. There is a passage in 1 Peter that states.
Concerning this salvation, the prophets, who spoke of the grace that was to come to you, searched intently and with the greatest care, trying to find out the time and circumstances to which the Spirit of Christ in them was pointing when he predicted the sufferings of Christ and the glories that would follow (1 Peter 1:10,11).
Since the Holy Spirit is called the "spirit of Christ" they must be the same person. The Holy Spirit, therefore, is merely another name for Christ Himself.
The Holy Spirit and Jesus Christ are distinct persons. The Spirit of Christ may just be another designation for Jesus or a way of explaining the ministry of the Holy Spirit – it does not mean they are the same person.
When the Helper comes, whom I will send to you from the Father, the Spirit of truth who proceeds from the Father, he will testify about me (John 15:26).
There was an early heresy in the church known as Binitarianism. Binitarianism is a belief in the Deity of the Father and Son but not the Holy Spirit. It taught that the Holy Spirit was actually another name for Jesus. The term, "Spirit of Christ" is used twice in the New Testament and it was assumed by some that the Holy Spirit and the Spirit of Christ are the same person – Jesus. However with some much evidence that the two are distinct persons there is much simpler explanations of the meaning of the phrase. The Binitarian heresy never gained much acceptance.