I would say that the answer depends on who you ask.
I think of the difference as being one of granularity and role. A software component to my understanding is a self-contained entity with a well-defined (and preferrably stable) interface that interacts with the remaining parts of a system, and which has significant meaning from a system architecture point of view. An example would be a data access abstraction layer.
A module to me would rather be a deployable source code bundle containing code which shares a common purpose, but doesn't perform any significant role in the system (which means replacing it would not require changes to the system's overall architecture). An example would be a JSON serializer in a web service.
