Where the Classic Protestant (i.e. Lutheran) differ from RCC idea of justification is where this justification happens. Does this happen in God or in the sinner? In the former,it happens in God's heart, it is the treatment or the verdict that one is righteous. In the latter, the righteousness happens in the sinner. The former is into 'gratia imputata' (grace imputed), the latter is into 'gratia infusa' (grace infused). There is big difference, the former is crediting into one's account. The latter is infusing strength into one's being. My RC friends can correct me if that is no longer the teaching of Mother Church. I have been away now more than half of my life, so I do not know now what is going on.
My real point is to distinguish between redemption and justification. Technically they are related but categorically not the same. The effect to us is the same i.e. we are set free to go in peace, but what happens prior to the effect are distinguishable.
Most use court room scenario to illustrate what is going on so I will try it anyway knowing that all analogies eventually are weak and when stretched will and do fail. However, in both cases I will show that 'gratia infusa' does not come into play whatsoever.
Here is how I look at redemption:
We are accused by the Tax Office of not paying taxes and we are brought court and face the judge/magistrate. The Tax Office shows the records that we have missed consistently paying our income taxes. The judge sees the evidence, and is about to pass his verdict of guilty calling on the sheriff to confiscate our assets, and throw us to jail. But just before he does it, someone (Jesus) steps in pays our arrears/debts. What does the judge do? He has to let us go because we owe nothing anymore. It got paid on our behalf. Here we are dead guilty and there is proof of it, but we are being set free because one payed for what we are guilty of.
Try this for justification:
The Tax Office like above, brings us to court accusing us of not paying our taxes. However, when the judge asks for proofs of missing tax payments, the Tax Office could not produce the records against us. The records went missing. What doe the judge do? He has to treat us as if we are righteous, there is no evidence to pass a verdict of guilty. A man is presumed innocent unless proven guilty, correct? Correct. There is no proof to convict us, hence, he has to let us go because the evidence against us could not be found. What is the judge to do? Nothing but to pronounce us as innocent. In this case, there is no implication that we are not guilty, it is just that there is no evidence beyond reasonable doubt to convict us.
Romans 4:5 And to the one who does not work but(E) believes in[b] him who justifies the ungodly, his faith is counted as righteousness,
Justification is what God does when we are brought to faith in that redemption provided by Jesus. Redemption is God forgiving us, but at the same time through faith, God presumes us as innocent as if we never missed paying our tax arrears at any time, he presumes us as having perfectly obeyed his Laws.
So in both cases there is no infused righteousness, in both cases, it is imputed righteousness, it is the righteousness through another.
Here is the kicker...
I run my own business and tax paying for me is a never ending activity. How I wish the above were the same in my relation to the Tax Office.