The interaction potentials between the ground state S(P-3) atom and rare gas atoms Rg (He, Ne, Ar, Kr, and Xe) in (3)Pi and (3)Sigma(-) states are calculated ab initio using an unrestricted CCSD(T) level of theory and extended correlation consistent basis sets augmented by bond functions. For NeS, the effects of extending the basis set, of a more accurate treatment of triple excitations within the coupled cluster method, and of the frozen core approximation are analyzed. The spin-orbit interaction is taken into account by the commonly used atomic model, whose validity is verified by the direct ab initio calculations of spin-orbit coupling matrix elements. The ab initio potentials are tested in the calculations of the absolute total scattering cross sections measured in molecular beams and compared with the potentials derived from the same data. This comparison, along with an analysis in terms of correlation formulas, proves the high accuracy of ab initio potentials and characterizes the sensitivity of scattering cross sections to the properties of interaction potentials. Both ab initio and scattering derived potentials are implemented in the study of inelastic fine structure transitions in S+Rg collisions. The relaxation rate constants are calculated and compared with those for O+Rg collisions.