The magnetocaloric effect and magnetization processes of the extended Ising model on the 3-dimensional octahedral lattice are studied by the classical Monte Carlo method with Metropolis algorithm. It is shown that different combinations of antiferromagnetic and ferromagnetic nearest-neighbor interactions J1 and J2 (in particular J1=−1, J2=1 and J1=−1, J2=−1) lead to the fundamentally different magnetic behaviors at nonzero temperatures, despite the fact that zero-temperature magnetization curves have exactly the same form. The reason is that the spin configurations forming zero-temperature magnetization plateaus for both J2=−1 and J2=1 are different, and different are also their temperature evolutions (controlled by calculations of in-plane and inter-plane sublattice magnetizations), which lead to different results for the magnetic entropy change (the magnetocaloric effect). Due to this fact a much higher positive entropy change is observed for the ferro-antiferromagnetic system compared to the pure antiferromagnetic system.