to set right: to establish what is just between parties, whether by judging, arguing a case, correcting with words, or disciplining
At its heart this verb is about getting to what is right and making it stick. The same act can take very different forms depending on who is doing it and to whom, which is why English Bibles translate it so many ways.
In a legal setting it means to decide a case, to act as the arbiter who weighs two sides and settles the matter fairly. Closely related is the courtroom sense of pressing one's own argument: to make a case, to reason a dispute out into the open. When the same energy is aimed at a person who has done wrong, it becomes correction: to point out the fault plainly, to reprove. And when correction goes beyond words into actual consequences, it shades into discipline: to chastise, the way a parent corrects a child for the child's good.
These senses are not separate words but points along one line. The thread running through all of them is a confidence that there is a right answer and that bringing it to light, by verdict, by argument, by rebuke, or by discipline, is an act of care rather than mere conflict. That is why the wisdom writers can say that the one who corrects you is your friend, and why being corrected by God is treated as a sign of love.