Comments on yesterday's "This love must be perceived" post point out that there are several different forms of correction, which, since they differ in the end sought, may also differ in the means used.
Admonishment, which I usually have in mind when speaking of "fraternal correction," seeks the elimination (or at least reduction) of a moral fault. The Church has a lot in Her treasuries that deals with admonishment of sinners, from Jesus' observation about the speck and the plank to St. Ignatius' comments and beyond. It's a spiritual work of mercy, but a particularly dicey one to do properly.
Instruction, another spiritual work of mercy, has as its end the correction of an intellectual fault. Where you admonish the sinner for doing something wrong, you instruct the ignorant for thinking something wrong -- or, perhaps more commonly, for not thinking something right. In a comment below, Christine brought up the example of correcting an untruth being spread by another, where you're not so much concerned with instructing the person teaching the untruth as with instructing those who might come to believe it.
Kathy pointed out another form of correction, "intended to change a wrong course of action." Here the end sought is purely external, and I'm sure there's a better term than resistance.