Martin Luther transformed Paul’s teaching about justification into a Protestant dogma about salvation. For Luther, salvation meant being saved from his guilt through the forgiveness found only in Christ’s death. This salvation was then equated with justification, understood as Christ’s righteousness (especially his sacrificial death) being imputed to the sinner–who then continued to be a sinner, albeit a justified sinner, a saved sinner.
The result is a long history of Protestant churches who preached “cheap grace.” The grace of justification could be received by simple confession of sin and belief in Jesus’ death as the means of becoming righteous. Accept Jesus as your personal Savior and your sins will be forgiven and you will be saved for eternity.
Luther was the first to separate justification (and salvation) from regeneration. One could become a Christian with no expectation of being transformed by God into a new creation, into a child of God who has the Spirit and is led by the Spirit of Christ. Luther’s reductionism isolated a partial view of justification (“reckoned as righteous”) to the point that Paul’s full teaching on righteousness/justification was downplayed. Thus Rom. 3 and 4–about justification through Christ’s death and Abraham’s justification of being reckoned as righteous–were elevated far above Rom. 2 and 6.
For in Rom. 2:13 Paul writes that it is the doers of the law (of Moses) that will be justified. This relates to final judgment, a final reckoning, but note that it takes seriously what one does. God’s righteous judgment will give to every one according to his works, to what one has done (2:5-6). In Rom. 6:4 Paul says baptism (the very beginning of being a Christian) includes dying and rising with Christ, with the result that one then walks according to a new way of life. Such a one is no longer enslaved by sin; instead, having died with Christ, one is “freed” from sin (6:6-7). The Greek word translated “freed” in many translations (in 6:7) is the same word translated as justified earlier in Romans. Even in Rom. 3 justification is linked with “redemption,” a word used especially for being freed from slavery (3:24). In Rom. 6:12-23 this new life is a life of righteousness and sanctification/holiness; having been set free from slavery to sin, one can now–through the power of God’s grace–become obedient to the teaching of Paul and Christ (who affirm only a small part of the law of Moses).
Rom. 8 is a beautiful commentary on Rom. 5:6 (God’s love has been poured into our hearts through the Holy Spirit which has been given to us). Because of this powerful grace of the Spirit, the “righteous requirement” of the law (of Moses), namely, “love” (as summarized by Jesus–love your neighbor–and by Paul, in Rom. 13:8-10) can be fulfilled in us, who walk according to the Spirit. This is so important to simply being a Christian that Paul can say in Rom. 8:9 that “anyone who does not have the Spirit of Christ does not belong to him.” So, “all who are led by the Spirit of God are children of God” (8:14).
All of this is what Paul means by righteousness and salvation–and justification.