We investigate the quenching properties of central and satellite galaxies, utilizing the halo masses and central-satellite identifications from the SDSS galaxy group catalog of Yang et al. We find that the quenched fractions of centrals and satellites of similar stellar masses have similar dependence on host halo mass. The similarity of the two populations is also found in terms of specific star formation rate and 4000 AA break. The quenched fractions of centrals and satellites of similar masses show similar dependencies on bulge-to-total light ratio, central velocity dispersion and halo-centric distance in halos of given halo masses. The prevalence of optical/radio-loud AGNs is found to be similar for centrals and satellites at given stellar masses. All these findings strongly suggest that centrals and satellites of similar masses experience similar quenching processes in their host halos. We discuss implications of our results for the understanding of galaxy quenching.