Our Gemara on Amud Aleph states that a convert is considered as if he or she are newly born. This is not just a metaphor, but actually of halakhic significance, removing genetic relatives from the prohibited sexual relations, should they both convert. (They are still prohibited rabbinically because it would have the appearance of impropriety.) A person can make such a major change in commitment and attitude that he actually becomes a different person. There is a similar idea expressed in Gemara Yoma (86b), that repentance out of love not only erases sin, but even turns sins into merits.
Rav Tzaddok MiLublin (Resise Layla 41) compares and contrasts these two concepts. The Gentile who converts has an ability to make a fresh start by virtue of his new commitment. However, the Jew has an additional power. Even when he sins, he is still a Jew and God walks with him. It is unfathomable, that even within his sins, there isn’t some spark of redeeming value or purpose. Thus, when he repents out of love, the malignant intent is retroactively rectified, and what remains is the portion of the sin that had some value and purpose, which now becomes considered as a merit. This is along the lines of what Rav Tzaddok says in Tzidkas Hatzaddik (139) says, that everything is the will of God, even sin. When one repents and refines his intentions to only serve God, then the impure intention is removed from the sin and only the will of God remains, thus it is a merit. (Obviously, Rav Tzaddok holds that one must always resist sin with all his ability. The idea that even sin is the will of God is a post-facto discussion.)
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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