The magnetism of FeRh (001) films strongly depends on film thickness and surface terminations. While the magnetic ground state of bulk FeRh is G-type antiferromagnetism, the Rh-terminated films exhibit ferromagnetism with strong perpendicular magnetocrystalline anisotropy whose energy +2.1 meV/whitesquare is two orders of magnitude greater than bulk 3d conventional magnetic metals (whitesquare is the area of a two-dimensional unit cell). While the Goodenough-Kanamori-Anderson rule on the superexchange interaction is crucial in determining the magnetic ground phases of FeRh bulk and thin films, the magnetic phases are the results of interplay and competition between three mechanisms-the superexchange interaction, the Zener-type direct interaction, and energy gain by Rh magnetization.