The two phrases are different and teach different doctrines. I'll try to be short.
Galatians 2:16, Knowing that a man is not justified by the works of the law, but by the faith of Jesus Christ, even we have believed in Jesus Christ, that we might be justified by the faith of Christ, and not by the works of the law: for by the works of the law shall no flesh be justified.
This glorious Scripture establishes the foundational truth of the gospel that you don't get in any modern versions, instead using faith in Christ. God's word declares that man can only be justified by the faith of Jesus Christ, not by works of the law.Galatians 2:20, I am crucified with Christ: nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh I live by the faith of the Son of God, who loved me, and gave himself for me.
The Holy Spirit wrote that the Apostle Paul and all believers are crucified with Christ and now we live by the faith of the Son of God. The believer does not live by his own faith as under the law.
Romans 3:22, Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe:
The righteousness of God is not by my faith in Jesus Christ, but the faith of Jesus Christ. It's all about Jesus Christ. Can you see how enept this makes God's word?
The faith of Christ is given to those that believe His gospel. Through belief in the gospel, one is justified by the faith of Christ. Remember, faith without works is dead. Christ's faith is not without works. Look at the cross! My individual faith could not possibly saved me. Christ's faith never waivers! Praise the Lord!
James 2
21 Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar?
22 Seest thou how faith wrought with his works, and by works was faith made perfect?
23 And the scripture was fulfilled which saith, Abraham believed God, and it was imputed unto him for righteousness: and he was called the Friend of God.
24 Ye see then how that by works a man is justified, and not by faith only.
This is not Church Age doctrine. Abraham was justified by works when he offered up Isaac. The Scripture that said Abraham believed God and it was imputed unto him for righteousness, Gen.15, was not fulfilled until seven chapters later in Gen. 22. It took works to fulfill it. The Church Age believer is not justified by any works of their own but by faith only, Romans 4. The works have been done! We need to just believe the gospel of Christ and His faith is imputed to us! Christ's faith, what we are justified by, is not without works. Our individual faith has nothing to do with our justification before men or God.