Module might be an overloaded term, so much that Wikipedia describes it under the term Modular Programming when discussing its use relative to software. They discuss it in terms of structured programming which was based on a top-down design approach. Key characteristics of modularity related to the use of low coupling and high cohesion.
My usage has been that in a language like C or even C++, a module is related to defining a separately compiled unit from a source file (.c or .cpp) and typically one associated header file (.h). Other languages use module as a description, and the language Modula-2 put structuring around modules front and center in its name and its approach.
Historically, module has some other implications as were described in the D.L. Parnas paper "On the Criteria to be Used in Decomposing Software into Modules". He is primarily concerned with discussing benefits of replacing functional decomposition with data oriented decomposition which was a big step toward our present state of the art which is object oriented decomposition.
Object oriented languages are organized around classes, so maybe the term module is less important and less precise in that context.