It's a little deeper then that. Remember Abraham had his own righteousness through the faith he had in the LORD, no one teaching him, not one example; hence blind faith of a pure heart. Remember the old testament, was by faith and your works. That's why you read accounted to him.
Galatians 3: 6Even as Abraham believed God, and it was accounted to him for righteousness. 7Know ye therefore that they which are of faith, the same are the children of Abraham. 8And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed. 9So then they which be of faith are blessed with faithful Abraham.
So then this isn't a subtle difference in meaning. In your heart you are broken (contrite), because you know you're going to hell. And because of this you've had godly sorrow to repent, amd all this has brought you to believe in something you can't see but hope for (faith in CHRIST), and it's called baptism. It's righteousness because as Abraham you believed blindly with a pure heart what is right the gospel vs the law as in the past. See reference verses 3 and 4 of the same changer 10.
And to give you more of a wonder to think of, the first paradise was called Abrahams bosom for this reason.
Your question is an awesome one because it has so much in it, you could right a book on it alone.
Hope this helps, praise our FATHER: JESUS CHRIST the ALMIGHTY!