22 Even [de] the righteousness [dikaiosune] of God [theos] which is by [dia] faith [pistis] of Jesus [Iesous] Christ [Christos] unto [eis] all [pas] and [kai] upon [epi] all [pas] them that believe [pisteuo]:
for [gar] there is [esti] no [ou] difference [diastole]: KJV-Interlinear
righteousness of God through faith in Jesus Christ for all who believe. For
there is no distinction: ESV
The righteousness of God, and faith in Christ are two phrases that mean exactly the same thing.
Paul has already pointed out that circumcision is not the means of salvation, but faith is.
When Abraham believed, then the righteousness of God was imputed to him because of that faith. That was years before Abraham was circumcised. So circumcision or any other thing that man could claim credit to, are invalid.
Works are not and never will be, a means of salvation, nor even connected with faith.
The only work that is legitimate, is the work of Christ, for it is real and true and it accomplishes something, namely the payment and removal of sin and then the way of salvation.
Mans work or works, accomplish nothing except to become a distraction away from reality and truth.
Gods righteousness and faith are one and the same. Gods righteousness is sinless perfection, and faith places man in the same sinless environment at the moment of salvation.
Of course people commit sins after salvation, and then the issue is not belief but confession, which is the believers version of faith or recognition of sin in his own life, before God. Therefore God is faithful and cleanses the unrighteousness and restores us back into fellowship with Him. That provides the means of maintaining a functional spiritual life.