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 by showing that 5-dimensional general relativity is equivalent to General Relativity and classical Electromagnetism in 4 dimensions. Supergravity goes a step ahead by also unifying the weak force, the strong force, and fermionic matter. Supersymmetry is required for this.
11-dimensional supergravity is the low-energy classical limit of M-theory.