If you add functionality to Phorum by providing extra scripts that go in the Phorum install directory and/or extra templates that need to be added to the main template directory (templates/templatename/...), then we talk about an add-on.

For Phorum 5.0, this was a pretty common thing to do. For Phorum 5.1 and up, a special script was added for being able to implement addon code fully through a module. Therefore, there is no real need anymore for writing add-ons: addon.php.