“I have been crucified with Christ. It is no longer I who live, but Christ who lives in me. And the life I now live in the flesh I live by faith in the Son of God, who loved me and gave himself for me.” (Galatians 2:20, ESV)
Here Paul is explicitly speaking of our union with Christ. Paul describes it as Christ actually living in the believer. This, of course, doesn’t mean that Christ mystically drowns out the personality of the believer turning him into a hypnotized subject at best or a programmed robot at worst. Rather, this reminds us that Christ is the source of new spiritual life within us. It is only through him that we now have a spiritual pulse and do things like “repent” and “believe.”
Paul goes on to say that he is living by “faith in the Son.” Usually we think of this verse as referring to our faith in the person and work of Jesus being the driving force behind our Christian life. Our active faith in the person and work of Christ is certainly an important part of the Christian life, but I don’t think that is what Paul is talking about here. Here when Paul says “faith in the Son” he is talking about the faith that we have only because of our Union with Christ. Instead of our active faith being the driving force of our lives, Paul is saying that the faith that has been created through union with Christ is the driving force of our lives. The difference is subtle, but it’s there.
Really the difference is in the source of the faith and subsequent life. If active faith in Jesus is what Paul is talking about then the life you live is driven by power of your faith. That completely contradicts the point that Paul is making in this verse. Paul’s point is that Jesus is the source of life; he’s the driving force behind your faith and Christian walk. He’s the source of the faith that leads you. That is why Paul says that he lives by “faith in the Son.” As Dr. MacArthur puts it,
That is why, the apostle continues, the life which I now live in the flesh I live by faith in the Son of God. The true Christian life is not so much a believer’s living for Christ as Christ’s living through the believer. Because in Christ “all the fulness of Deity dwell-s in bodily form” (Col. 2:9), the fulness of God also dwell-s in every believer, as “partakers of the divine nature” 
The faith that identifies us to Christ and the salvation that he has accomplished comes to us because of our union with Christ.
 John MacArthur, Galatians (Chicago: Moody Press, 1996), 60.