  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]
