Catholic encyclopedia: https://www.newadvent.org/cathen/04394a.htm

Fraternal correction is here taken to mean the admonishing of one’s neighbor by a private individual with the purpose of reforming him or, if possible, preventing his sinful indulgence. This is clearly distinguishable from an official disciplining, whose mouthpiece is a judge or other like superior, whose object is the punishment of one found to be guilty, and whose motive is not so directly the individual advantage of the offender as the furtherance of the common good. That there is, upon occasion and with due regard to circumstances, an obligation to administer fraternal correction there can be no doubt. This is a conclusion not only deducible from the natural law binding us to love and to assist one another, but also explicitly contained in positive precept such as the inculcation of Christ: “If thy brother shall offend against thee, go, and rebuke him between thee and him alone. If he shall hear thee, thou shalt gain thy brother” (Matthew 18:15).

Aquinas on topic: https://www.newadvent.org/summa/3033.htm