In mathematics|lang=en terms the difference between superalgebra and supermodule
is that superalgebra is (mathematics) a type of algebra used in supersymmetry while supermodule is (mathematics) a particular module over a superring or superalgebra.
As nouns the difference between superalgebra and supermodule
is that superalgebra is (mathematics) a type of algebra used in supersymmetry while supermodule is (mathematics) a particular module over a superring or superalgebra.