Rectify is a fine translation, but there’s some ambiguity about it. It makes make right. But what do you mean by right?
The Protestant tradition says declare righteous, with a forensic tilt, meaning declare not guilty before God. In Protestant theology this is something that happens once (arguably, at Jesus’ death) and is permanent. Rectify is fine for this, as it means make right with God.
The Catholic tradition says make righteous, with a focus on the Christian life. So it’s a continuing process, which can be interrupted. This can still be called rectification, with the understanding that rectification is an ongoing process.
This is in some sense a false dichotomy. At least in the Protestant understanding there are both permanent and developing aspects of the process of salvation. Hence the use of the term “sanctification” to represent the ongoing process. (I note this this isn’t Biblical language. Sanctification is used differently in the NT. I generally speak simply of the Christian life.)
There’s a third perspective which to my knowledge is fairly recent (though perhaps this isn’t true in the East). That’s the covenantal context. Paul was using that perspective, because he was looking at how God worked with Jews and Gentiles over history, at the grafting of Gentiles into the covenant. From this perspective, rectification means making someone a member in good standing of the covenant people. (However I would agree with Wright that in Romans it’s often recognition that someone is a member of the covenant.) But this shares a lot with the classical Protestant concept, because it’s still about our status before God, and it’s permanent (except in unusual situations that I’d categorize as apostasy).
Our theology tends to come out of our experience. Luther found that he was unable to have any confidence that he was actually accepted by God. If your whole idea about salvation is an ongoing process that can have setbacks, and requires you to deal properly with every sin, and if you’re sensitive to the severity of sin, it’s easy to be afraid that you haven't fully dealt with your sin, you aren't saved, and eventually, that God doesn’t care about you. This isn’t just a late medieval problem, nor is it only a result of Catholic theology. We see the same thing every day in CF’s Christian Advice and other places, and in CF it’s largely people from a Protestant background.
So historically, for Protestants, justification represents our status as people of God, based on God’s commitment to save his people, not our own moral success. Of course the other side is still there: we’ll be judged for how we respond to Christ’s call. But when we fail, we fail as disobedient children, not as people that God has abandoned.
In the West, both during Luther’s tine and today, Christianity has tended to focus on avoiding hell. For many Christians today, that’s all Jesus is good for. They reinterpret all of his statements about the Kingdom as just about avoiding hell. That’s a terrible distortion of his message. For me, justification is a way of dealing with this. It says that our status as being acceptable to him is something we can trust. It’s based on Christ’s death for us. Our whole Christian lives can’t be devoted just to doing what we need to do to stay out of hell.
I previously observed that Catholic teaching places more emphasis on Justification meaning "made righteous" or "made just" and the idea is that not only is there a legal idea in the word "justification" but there is also a real change in the people who are said to be "justified" and that real change is that they become - progressively - more and more just and righteous when they make good use of the graces that God gives to them in their lives. And because Catholic tradition keeps both the idea of legal and of actual change of status in its use of "justification" it follows that Catholic theology also places emphasis on real change in one's way of life and attitudes and words and doings as the actual meaning of "justification".
As you noted in holy scripture "sanctification" has a meaning rather distinct from its common use in Protestant theologies. In the holy scriptures sanctification is about being separated from the world and reserved for God's purposes. There is a moral aspect to sanctification but the primary emphasis is on separation. The use that is common in Protestant theologies is quite unlike the use in the holy scriptures insofar as Protestant theologies place primary (almost exclusive) emphasis on moral holiness (goodness). That is, in part, why Protestant theologies tend towards a sharp distinction between justification and sanctification.
In Catholic theology "sanctification" retains the idea of separation from the world. The moral dimension is not forgotten but the primary emphasis is on separation. That is why you can hear Catholics speak of "the sanctified life" by which is meant life in separation from worldly concerns such as one might experience in a monastic discipline. You can also hear Catholics speak of a sanctified person by which is meant someone who is godly, good, and separate from worldly concerns.
The council of Trent wrote of its intention "to expound to all the faithful of Christ the true and sound doctrine touching the said Justification; which (doctrine) the sun of justice, Christ Jesus, the author and finisher of our faith, taught, which the apostles transmitted, and which the Catholic Church, the Holy Ghost reminding her thereof, has always retained; most strictly forbidding that any henceforth presume to believe, preach, or teach, otherwise than as by this present decree is defined and declared."
The council then went on to write
CHAPTER I.
On the Inability of Nature and of the Law to justify man.
The holy Synod declares first, that, for the correct and sound understanding of the doctrine of Justification, it is necessary that each one recognise and confess, that, whereas all men had lost their innocence in the prevarication of Adam-having become unclean, and, as the apostle says, by nature children of wrath, as (this Synod) has set forth in the decree on original sin,-they were so far the servants of sin, and under the power of the devil and of death, that not the Gentiles only by the force of nature, but not even the Jews by the very letter itself of the law of Moses, were able to be liberated, or to arise, therefrom; although free will, attenuated as it was in its powers, and bent down, was by no means extinguished in them.
So no one can rightly contend that Catholic believe that anybody (Jew of Gentile) saves themselves. The council continued writing
CHAPTER II.
On the dispensation and mystery of Christ's advent.
Whence it came to pass, that the heavenly Father, the father of mercies and the God of all comfort, when that blessed fulness of the time was come, sent unto men, Jesus Christ, His own Son-who had been, both before the Law, and during the time of the Law, to many of the holy fathers announced and promised-that He might both redeem the Jews who were under the Law, and that the Gentiles, who followed not after justice, might attain to justice, and that all men might receive the adoption of sons. Him God hath proposed as a propitiator, through faith in his blood, for our sins, and not for our sins only, but also for those of the whole world.
CHAPTER III.
Who are justified through Christ.
But, though He died for all, yet do not all receive the benefit of His death, but those only unto whom the merit of His passion is communicated. For as in truth men, if they were not born propagated of the seed of Adam, would not be born unjust,-seeing that, by that propagation, they contract through him, when they are conceived, injustice as their own,-so, if they were not born again in Christ, they never would be justified; seeing that, in that new birth, there is bestowed upon them, through the merit of His passion, the grace whereby they are made just. For this benefit the apostle exhorts us, evermore to give thanks to the Father, who hath made us worthy to be partakers of the lot of the saints in light, and hath delivered us from the power of darkness, and hath translated us into the Kingdom of the Son of his love, in whom we have redemption, and remission of sins.
CHAPTER IV.
A description is introduced of the Justification of the impious, and of the Manner thereof under the law of grace.
By which words, a description of the Justification of the impious is indicated,-as being a translation, from that state wherein man is born a child of the first Adam, to the state of grace, and of the adoption of the sons of God, through the second Adam, Jesus Christ, our Saviour. And this translation, since the promulgation of the Gospel, cannot be effected, without the laver of regeneration, or the desire thereof, as it is written; unless a man be born again of water and the Holy Ghost, he cannot enter into the Kingdom of God.
I quoted from the council of Trent because it was called specifically to deal with reform in the Catholic Church and to combat the heresies that were propagated among Protestants at the time of the "Protestant Reformation". It ought to be evident that the fathers at the council of Trent saw their teaching as the teaching of Christ. And it ought to be clear that the council fathers at Trent did not teach that anybody saved themselves, though some in this thread have repeatedly and incorrectly asserted otherwise.