There are two holy spirits in the gospels.
Understanding the spirit of God and the Spirit of Christ in the gospels is challenging.
First, because two holy spirits are described: the Spirit of Christ that came upon Mary and the spirit of God that was first put on Christ. Both are called “holy spirit.”
And of course, it is difficult to understand how the Spirit of Christ can be manifest in Christ and still be active in other people. The Holy Spirit that came on Mary was also in Elizabeth and John the Baptist. Paul said that Jesus was only “found in appearance as a man” (Philippians 2:8), “revealed in the flesh” (1 Timothy 3:16), just as the Spirit of Christ was only found in appearance as an angel in the Old Testament. This was dramatically illustrated for us in the first Chapter of Revelation, where the Spirit of Christ appeared as the Angel of God and the Son of Man at the same time.
Another challenge of the gospels is that the expression “the spirit” describes the spirit of God that led Jesus into the wilderness, and the Spirit of Christ in the kingdom of heaven, beginning in Matthew 5:2, “Blessed are the poor in the Spirit (τῷ πνεύματι) for theirs is the kingdom of heaven.”
After the Day of Pentecost, “spirit” without the article only described the spirit of God. John said, “spirit was not yet given because Jesus was not yet glorified” (John 7:39).
In Matthew 1:20, we read “That which is conceived of spirit is holy,” and in Matthew 22:43, Jesus said, “How then does David in spirit call Him, Lord.” Both verses describe the Spirit of Christ.