Nematicity and magnetism are two key features in Fe-based superconductors, and their interplay is one of the most important unsolved problems. In FeSe, the magnetic order is absent below the structural transition temperature T_str=90  K, in stark contrast to the fact that the magnetism emerges slightly below T_str in other families. To understand such amazing material dependence, we investigate the spin-fluctuation-mediated orbital order (n_xz≠n_yz) by focusing on the orbital-spin interplay driven by the strong-coupling effect, called the vertex correction. This orbital-spin interplay is very strong in FeSe because of the small ratio between the Hund’s and Coulomb interactions (J¯/U¯) and large d_xz, d_yz-orbital weight at the Fermi level. For this reason, in the FeSe model, the orbital order is established irrespective of the fact that the spin fluctuations are very weak, so the magnetism is absent below T_str. In contrast, in the LaFeAsO model, the magnetic order appears just below T_str both experimentally and theoretically. Thus, the orbital-spin interplay due to the vertex correction is the key ingredient in understanding the rich phase diagram with nematicity and magnetism in Fe-based superconductors in a unified way.