Add-on and plug-ins are two widely used terms in browsers. Both the terms boost the performance of browser. In Firefox you install add-ons to add extra features as well as add plug-ins to add some missing functionalities. Despite of their matching properties, both the terms are not same.
Plug-in is a complete program and add-on is not a program. For example Flash is an plug-in which is a complete program. Flash player is required to play a video which is made by a company known as Adobe. Also Java is a plug-in made by Sun Microsystem which is used to run programs based on Java. Plug-in is not bounded for browsers only. Flash can be installed in computers to play flash files. Similarly Java can be installed to run Java files.
On the other hand add-on is not a complete program. It is used to add a particular functionality to a browser. If you suppose to install add-on on other work environment, say, your operating system, you can’t do it. It means, add-ons are limited to a certain boundary.
These days there are many browsers which comes with add-on features. Firefox, Chrome, Internet Explorer, Safari and the recently born RockMelt has add-on facility. In Chrome add-on is known as extension. There is no difference between add-on and extension. Both are the same terms used differently in different browsers.