By comparing a collisionless cosmological N-body simulation (DM) to a smoothed particle hydrodynamics simulation (SPH) with the same initial conditions, we investigate the correspondence between dark matter subhalos produced by collisionless dynamics and galaxies produced by dissipative gas dynamics in a dark matter background. When galaxies in the SPH simulation fall into larger groups and become satellites, they retain local dark matter concentrations (SPH subhalos) whose mass is typically 5 times the galaxy baryonic mass (compared to the simulation's universal ratio Ω_dm/Ω_b ≈ 7.5). The more massive subhalos of the SPH simulation generally have corresponding subhalos of similar mass and spatial position in the DM simulation; at lower masses, there is still fairly good correspondence, but some DM subhalos are in different spatial positions and some have suffered tidal stripping or disruption. The halo occupation statistics of DM subhalos—the mean number of subhalos, pairs, and triples as a function of host halo mass—are very similar to those of SPH subhalos and SPH galaxies. The gravity of the dissipative baryon component amplifies the density contrast of subhalos in the SPH simulation, making them more resistant to tidal disruption. Relative to SPH galaxies and SPH subhalos, the DM subhalo population is depleted in the densest regions of the most massive halos. The good agreement of halo occupation statistics between the DM subhalo and SPH galaxy populations leads to good agreement of their two-point correlation functions and higher order moments on large scales. The depletion of DM subhalos in dense regions depresses their clustering at R < 1 h^-1 Mpc. In these simulations, the "conversation" between dark matter and baryons is mostly one-way, with dark matter dynamics telling galaxies where to form and how to cluster, but the "back talk" of the baryons influences small-scale clustering by enhancing the survival of substructure in the densest environments.