In mathematics|lang=en terms the difference between superring and supermodule
is that superring is (mathematics) a superalgebra over a ring while supermodule is (mathematics) a particular module over a superring or superalgebra.
As nouns the difference between superring and supermodule
is that superring is (mathematics) a superalgebra over a ring while supermodule is (mathematics) a particular module over a superring or superalgebra.