"Browser addon" is a generic term to cover both extensions to web browsers and plugins which are an older and more specific concept. Mostly used with regard to the Firefox web browser.
Browser plugins have existed since the days of Netscape and work on most web browsers.
Newer ways to add functionality to web browsers are generally refereed to as extensions and are specific to each individual browser platform.
The term "browser addon" is new cover term that can refer to both of the above and is currently mostly used in the context of the Firefox browser.