According to the literature statistics, only less than 10% of reported iterative learning control (ILC) methods have been devoted to the indirect approach. Motivated by the full potential of research opportunities in this field, a number of studies on indirect ILC were proposed recently, where ILC-based P-type control and learning-type model predictive control (L-MPC) are two successful stories. All indirect ILC algorithms consist of two loops: an ILC in the outer loop and a local controller in the inner loop. The local controllers are, respectively, a P-type controller in the ILC-based P-type control and a model predictive control (MPC) in the L-MPC. Logically, this leads to the question of what type of ILC should be chosen respectively for the two above-mentioned indirect ILC methods. In this study, P-type ILC and anticipatory P-type (A-P-type) ILC are studied and compared, because they are typical and widely implemented. Based on mathematical analysis and simulation test, it has been proved that the A-P-type ILC should be used in the ILC-based P-type control and while the P-type ILC should be used in the L-MPC. Furthermore, an improved L-MPC with batch-varying learning gain was proposed to handle the trade-off between convergence rate and robustness performance. The simulation results on injection molding process and a nonlinear batch process validated the feasibility and effectiveness of the proposed algorithm.