In my understanding—which I admit may be limited in this regard, hence why I'm asking here—although there is no strict or standardised set of definition(s) or distinction(s), a generally accepted perspective has, as is often the case, gradually taken form as computers have progressed over the years.
If I comprehend the subject correctly, the basic idea¹ nowadays is that extensions, apps, services, themes, and plugins that are not installed by default are distinct types of addons. Some examples, as well as a quick diagramme I constructed to illustrate my description, are below:
- Firefox Extensions
- Chrome Extensions
- Opera Extensions
- Firefox Apps (i.e., apps within the Firefox Marketplace
- Chrome Apps
- Chrome Themes
- Firefox Themes
- Personas (first changed to "Background Themes", now just "themes")
- Complete Themes
- Non-Default Plugins
- Certain programmes give the option to install plugins into one's browser to extend said programme'(s') functionality into said browser.
¹ Expectedly, there are some vague points where common demarcations are not quite so clearly known: for example, would a font be considered a system extension or, because it is something that is added on to the browser's set of capable functions would it be considered perhaps a type of plugin? Personally, because usage of said font(s) is typically not specific to just the browser, I don't think it would be. Although others' viewpoints may differ. There are undoubtedly other grey areas as well...