Satellite galaxies in rich clusters are subject to numerous physical processes that can significantly influence their evolution. However, the typical L* satellite galaxy resides in much lower mass galaxy groups, where the processes capable of altering their evolution are generally weaker and have had less time to operate. To investigate the extent to which satellite and central galaxy evolution differs, we separately model the stellar mass - halo mass (M* -Mh) relation for these two populations over the redshift interval 0 < z < 1. This relation for central galaxies is constrained by the galaxy stellar mass function while the relation for satellite galaxies is constrained against recent measurements of the galaxy two-point correlation function (2PCF). At z ~ 0 the satellites, on average, have ~10% larger stellar masses at fixed peak subhalo mass compared to central galaxies of the same halo mass. This is required in order to reproduce the observed stellar mass-dependent 2PCF and satellite fractions. At low masses our model slightly under-predicts the correlation function at ~1 Mpc scales. At z ~ 1 the satellite and central galaxy M*-Mh relations are consistent within the errors, and the model provides an excellent fit to the clustering data. At present, the errors on the clustering data at z ~ 2 are too large to constrain the satellite model. A simple model in which satellite and central galaxies share the same M*-Mh relation is able to reproduce the extant z ~ 2 clustering data. We speculate that the striking similarity between the satellite and central galaxy M*-Mh relations since z ~ 2 arises because the central galaxy relation evolves very weakly with time and because the stellar mass of the typical satellite galaxy has not changed significantly since it was accreted. [Abridged]
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