Supergravity is a classical supersymmetric unification theory. It appears in low-energy classical limits of string-theory.
kaluza-klein-Theory unifies classical general-relativity with Maxwell's classical electromagnetism (maxwell-equations) by showing that 5-dimensional general relativity is equivalent to 4-dimensional General relativity + 4-dimensional maxwell's classical electromagnetism. Supergravity goes a step ahead by also unifying the weak-force and strong-force. To do this, however, supersymmetry is also required. However, supergravity is a classical theory.
11-dimensional supergravity is the low-energy classical-limit of m-theory.