What is the difference between repentance coupled with the implementation of a worldly punishment and pure repentance between the servant and his Lord without the implementation of a punishment?

There is good in every course of action. Texts have been narrated commanding self-concealment upon committing a sin. Some scholars have inferred from this that concealment is commendable and better than confessing the sin to have the hadd punishment administered. Others have maintained that confession is better. A third group held that concealment is better for someone who is not known for committing such acts publicly. Al-Hafiz Ibn Hajar preferred that one who confesses to have the hadd punishment administered, out of an excessive desire for purification, is better than one who conceals it and repents privately between himself and his Lord. It is commendable for someone who falls into a situation like that of Ma'iz to repent to Allah Almighty, conceal themselves, and not mention it to anyone. And whoever becomes aware of such a matter should conceal it for them, not expose them, and not report it to the Imam. "All of this applies to one who is not openly defiant. As for one who openly displays lewdness and is defiant, I prefer exposing them and disgracing them so that they and others may be deterred." As for Al-Ghamidiyyah, her pregnancy became apparent, making concealment impossible due to the visible sign of indecency. What seems apparent is that concealment is commendable, and reporting it, with the intention of striving for purification, is more beloved.