We see from Calvin (Institutes III.3.3-4) what makes up the difference between true and false repentance. False or legal repentance is content merely to ask for the removal of punishment. They experience the consequences and judgment of God for their sin yet ask only for the removal of the consequences and judgment.
True repentance consists in the asking of the removal of sin, even more so, the desire to have a new heart, as David prayed in Psalm 51 “Create in me a clean heart”. Calvin shows the ancients stating that true repentance is wanting to be other than what they are. Here, this is clearly seen in that true repentance, despite the weakness of the flesh, comprehends the form of righteousness required and wishes to conform to that. The sinner recognizes that the issue of sin must be dealt with at its root in the heart, hence for the request for the removal of sin.
The contrast between the true and false repentance can be clearly seen. A unregenerate sinner will only be restrained in their sin by the active presence of God’s fury and anger. They dread not the sin of their own hearts but the displeasure brought on by their own sin. They care nothing of a changed heart, only insofar as it dispels God’s anger from them, that is to say, new behavior is useful only to deflect the judgment of God and no more.
The true penitent relents not just at the consequences but over the sin itself and their lack of conformity to God’s righteousness. Their whole object is not the pleasure of themselves but the pleasure of God and seeking to please him in all that they do. Hence the desire for the cleansing of the heart from sin. For, it is from the heart that the wellsprings of life flow and in order for the mind and the will to produce fruits of righteousness, the heart must be dealt with.
I do not doubt the weakness of even the penitent, for their is always mixture in all actions and thoughts of God’s children this side of heaven. But this truth will remain: that in the heart of the penitent they wish to be other than what they are so that they might please the Lord whom they love. Nothing is more grievous to them that to offend their master.