I'm using the term module to designate an area of functionality and/or the code that creates it. To exemplify, the header of a website could be considered a module. The header module would, in turn, be made up of other smaller pieces of functionality. For example, drop-down menus or search boxes. These nested pieces of functionality would be defined as components. Finally, our smallest items would be the child nodes that make up a component or module.
So, to reiterate:
A module is the widest, visually identifiable, individual section of functionality
Components are the nested pieces of functionality that are included within a module
Child nodes are the individual parts that go to make up a component (typically nodes in the DOM)
For brevity, for what follows, when I'm referring to modules, it could be a module or component. The difference from a ECSS authoring perspective is unimportant.