At low reaction energies, the Multi-Step Compound (MSC) reactions dominates over the Mutli-Step Direct (MSD) reactions. There is no sharp limit between the two types, because in MSD, at least one particle (nucleon) is highly excited to be in a continuum energy state; while in MSC all excited nucleons must remain in their bound states. In both, nuclear reaction is assumed to develop via particle-hole creation in a statistical process, described by few models. Depending on the type of the target nucleus and projectile, a proper choice between MSC or MSD can be made.
The original papers introducing the FKK theory (Feshbach-Kerman-Koonin), have detailed characterization of the two types, within you can find simple enough physical concepts. Please refer to the introductions of :