Notice how the Spirit is said to be distinct from Christ in this context and yet is also said to BE Christ
Rom 8:9 But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you. Now if any man have not the Spirit of Christ, he is none of his.
Rom 8:10 And if Christ be in you, the body is dead because of sin; but the Spirit is life because of righteousness.
Rom 8:11 But if the Spirit of him that raised up Jesus from the dead dwell in you, he that raised up Christ from the dead shall also quicken your mortal bodies by his Spirit that dwelleth in you.
Some folks would see this distinction in verse 11 and conclude that Christ can't be that Spirit or that the Spirit of Christ can't be the Spirit of God....because of the grammatical distinctions. Yet clearly the same Spirit is being refered to...How is it that a mere man can be in you all (Christians)? Unless by "Christ be in you" it is refering to the Spirit of God.
In this context then Christ is distinct from God and Spirit and yet Spirit of Christ is synonomous with Spirit of God and "Christ in you"