This build system overview is the best place to learn what a module is. Prior experience with programming will be useful, it’s not super detailed.
A plug-in is much more than a single module, with the primary goal being binary redistribution of a set of engine modules and/or engine content. So while an engine module will only ever contain code, a plugin can contain both code and content (uassets!). Plugins can also be distributed without source code, so if you want to distribute a binary version of a module, you would make a plugin that to do so. More details on plugins here.
If you just want to write some code and link in the UE4 codebase, make a module. If your aims are grander, look into plugins.