Inelastic scattering is common in molecular collisions. Any collision which leads to a chemical reaction will be inelastic, but the term inelastic scattering is reserved for those collisions which do not result in reactions. There is a transfer of energy between the translational mode (kinetic energy) and rotational and vibrational modes.
If the transferred energy is small compared to the incident energy of the scattered particle, one speaks of quasielastic scattering.