In one sense Jesus and the Holy Spirit are the same. But, in another sense they are not the same.  We would say that Jesus and the Holy Spirit both are divine in essence since they are members of the Trinity. So they are both God in nature. However, they are not the same person. A “person” can speak, has a will, recognizes others, etc. This qualifies as personhood. So, Jesus and the Holy Spirit are not the same (person).

The doctrine of the Trinity states that there is one God who exists in three distinct, eternal persons: The Father, the Son, and the Holy Spirit.  Though each member of the Trinity shares the same nature as being God (Ontological Trinity), they do not all have the same functions (Economic Trinity). For example, the word became flesh and dwelt among us as the person of Jesus (John 1:1,14). The Father did not do that, nor did the Holy Spirit. So, there is a distinction between them. Furthermore, Jesus said that he would send the Holy Spirit in John 15:26, “When the Helper comes, whom I will send to you from the Father, that is the Spirit of truth who proceeds from the Father, He will testify about Me.” So if the Holy Spirit and Jesus were the same, it would not be possible for Jesus to say he would be sending the Holy Spirit. Also, he referred to the Holy Spirit as “he” not “me.”

There are false groups who teach that the Trinity is not true and that God is a single person who manifests in different forms. These are oneness Pentecostal groups and they are not Christian in their teaching false doctrine.