As I said, it means more than that, not less than that as if forgiveness is excluded. When a person is justified, they are forgiven,, washed, cleansed, made new creations with new hearts and spirits, now children of God enabled by His grace to live as children of God should.
And justice is an appropriate translation there. Either way its all translation and interpretation unless we have the original manuscript and can speak the original language and can know the original author's intention.
The terms are just part of classical western scholarship where the Latin language and usage prevailed. Luther, commenting on his "Tower Experience" where he came to understand that "justice" as used in the bible was often referring to a good thing, the righteousness which He gives to man by faith (whether imputed or otherwise, incidentally), rather than strictly the source of judgment and condemnation. If you understand what really happened to Luther, he came to know that God is on our side even if he understood it imperfectly, as he claims that Augustine did.. This can take time in any case-we begin with the idea that God is angry, distant, aloof in His superiority, controlling, and perhaps preferring to send us to hell-sort of the attitude humans have with each other when we play God.
"I exalted this sweetest word of mine, "the justice of God," with as much love as before I had hated it with hate. This phrase of Paul was for me the very gate of paradise. Afterward I read Augustine's "On the Spirit and the Letter," in which I found what I had not dared hope for. I discovered that he too interpreted "the justice of God" in a similar way, namely, as that with which God clothes us when he justifies us. Although Augustine had said it imperfectly and did not explain in detail how God imputes justice to us, still it pleased me that he taught the justice of God by which we are justified."
While we work it out with Him, in fear and trembling. (Phil 2:12)