I am afraid that you need to explain your question a bit more, if I am to try to help you.
The usual distinction would be/could be in space. The long range relaxation could be identified with fast polarisation (value of the dielectric constant bellow 1 THz for example), involving all/many electrically active atoms/molecules of the system, while the localised polarization would be relaxation of one/few atoms/molecules. In nonlinear lattices it could be a relaxation of "breathers" (spatially localised,high amplitude and long lived excitations) or relaxation of a deep level (large lattice deformation) in monocrystalline Silicon.