The question here isnt really a PHP question, but I’ll give it a swing…
Modules/Plugins are generally equivalent terms - they use existing programming in the software to extend the original program’s abilities.
Addons are generally similar, though their operation is usually independent of the original program’s code.
Products (in terms of software) is… the actual original software.
In PHP terms - the Product (although it’s free) is PHP itself. Modules are abilities attached to the PHP execution (mysqli, zlib, etc etc). Addons doesn’t really have a PHP connotation i’m aware of…