As demonstrated in Paper I, the quenching properties of central and satellite galaxies are quite similar as long as both stellar mass and halo mass are controlled. Here we extend the analysis to the size and bulge-to-total light ratio (B/T) of galaxies. In general central galaxies have size-stellar mass and B/T-stellar mass relations different from satellites. However, the differences are eliminated when halo mass is controlled. We also study the dependence of size and B/T on halo-centric distance and find a transitional stellar mass (M$_{*,t}$) at given halo mass (M$_h$), which is about one fifth of the mass of the central galaxies in halos of mass M$_h$. The transitional stellar masses for size, B/T and quenched fraction are similar over the whole halo mass range, suggesting a connection between the quenching of star formation and the structural evolution of galaxies. Our analysis further suggests that the classification based on the transitional stellar mass is more fundamental than the central-satellite dichotomy, and provide a more reliable way to understand the environmental effects on galaxy properties. We compare the observational results with the hydro-dynamical simulation, EAGLE and the semi-analytic model, L-GALAXIES. The EAGLE simulation successfully reproduces the similarities of size for centrals and satellites and even M$_{*,t}$, while L-GALAXIES fails to recover the observational results.
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