Why Both the Spirit of God & the Spirit of Christ?
You, however, are not in the realm of the flesh but are in the realm of the Spirit, if indeed the Spirit of God lives in you. And if anyone does not have the Spirit of Christ, they do not belong to Christ. Romans 8:9 (NIV)
In brief, the Spirit of God indwells a person who has accepted the Lord Jesus as their savior. We are a sinner who needs salvation. How do we know if a person is saved? The person will show the Spirit of Christ in their lives. In other words, we will see a likeness of Jesus in the way that they live. We need to study the life of Jesus in order to show the Spirit of Christ in this world. When we observe a person showing the Spirit of Christ in their outward behavior, it is good evidence that the person has the Spirit of God in their inward life.
The Apostle Paul makes it clear that the evidence for true salvation and the indwelling of the Spirit of God is the manifestation of the Spirit of Christ in our daily lives.