The search direction is predictor step and corrector step?

This implementation is wonderful. I have read it in detail and I have one question.
I see from line 109 in " function [f, x, y, s, N] = mpcSol(A, b, c, param_in, Name)" that the search direction is predictor step and corrector step. But《Numerical Optimization》said the search direction is the correction step? Did I understand that correctly? And if so, do you think there are some benefits in your implementation?