We extend the abundance matching technique (AMT) to infer the satellite-subhalo and centralhalo mass relations (MRs) of local galaxies, as well as the corresponding satellite conditional mass functions. We use the observed galaxy stellar mass function (GSMF) decomposed into centrals and satellites and the Λ-CDM distinct halo and subhalo mass functions as inputs. We explore the effects of defining the subhalo mass, m sub , at the time of (sub)halo accretion (m acc sub ) versus defining it at the time of observation (m obs sub ); and we test the standard assumption that centrals and satellites follow the same MRs. We show that this assumption leads to predictions in disagreement with observations, specially when m obs sub is used. Instead, we find that when the satellite-subhalo MRs are constrained by the satellite GSMF, they are always different from the central-halo MR: the smaller the stellar mass, the less massive is the subhalo of satellites as compared to the halo of centrals of the same stellar mass. This difference is more dramatic when m obs sub is used instead of m acc sub . On average, for stellar masses lower than ∼ 2 × 10 11 M ⊙ , the dark mass of satellites decreased by 60 − 65% with respect to their masses at accretion time. We find that MRs for both definitions of subhalo mass yield satellite conditional mass functions (CSMF) in agreement with observations. Also, when these MRs are used in a halo occupation model, the predicted two-point correlation functions at different stellar mass bins agree with observations. The average stellar-halo MR is close to the MR of central galaxies alone, and conceptually this average MR is equivalent to abundance matching the cumulative total GSMF to the halo + subhalo mass function (the standard AMT). We show that the use of m obs sub leads to less uncertain MRs than m acc sub , and discuss some implications of the obtained satellite-subhalo MR. For example, we show that the tension between abundance and dynamics of Milky-Way satellites in the Λ-CDM cosmogony gives if the faint-end slope of the GSMF upturns to a value of ∼ −1.6.