Exact difference between add-ons, plugins and extensions - firefox

Question

What is the exact difference between plugins, add-on and extensions.
I have read a lot about this and confused,
For example see these four definitions:
1-fire-fox says "Add-ons is the collective name for extensions, themes and plugins" (see https://support.mozilla.org/en-US/questions/790919)
2-www.Differencebetween.net says "Plug-in and Add-on are simply extensions ... Plug-in is the term that is usually used when referring to third party software (interact with a certain program) like flash player ...
3- wikipedia (https://en.wikipedia.org/wiki/Plug-in_%28computing%29) says plugin are being deprecated.
4-I have read in another website that plugins are larger than add-ons and it consist add-on concept.
Also I have read the answer provided in firefox add-on vs. extensions vs. plugins and http://colonelpanic.net/2010/08/browser-plugins-vs-extensions-the-difference/
However I want to understand these differences especially in firebreath where plugins execute automatically through user's consent and add-on should install manually. Also I think plugin embed in htm page while add-on is in form of a separated file like xpi in fire-fox.
Any exact, comprehensive and precise definitions for these three concepts which emerge differences would be appreciated.

Answer 1

General rule of thumb:
Plugins
When you're talking about a web browser, a plugin talks about a NPAPI or similar plugin, which is specific to the page. IE doesn't support "plugins" per se, but they have activex controls which can fill a similar function, though there are also BHO (Browser Helper Object) ActiveX controls which are more similar to extensions. Thus we (the FireBreath team) usually use the term "plugin" to refer to something that works like a NPAPI plugin and the term "extension" to refer to something that works like a typical extension (firefox XPI, Chrome CRX, etc).
Plugins only know about the page they are in; they don't know anything else about the browser or what is loaded in other pages.
Plugins have been responsible for a lot of security problems, since they actually run native code. This has led to a lot of discrimination against them -- much of it deserved. Because of this, and because NPAPI is a royal pain in the neck (hence FireBreath was created), most browsers are trying to phase out plugins. Plugins should never be used unless there is no other way to solve your problem.
That said, there are a lot of cases where they are the only option.
Extensions
An extension is something that is specific to the browser, and they are a bit different on each browser, but tend to be able to learn more about the overall state of the browser; they may be automatically added to pages, accessible separately from a page, etc.
Add-ons
Add-on is more of a generic term which is used to mean a lot of different things. What it actually means just depends on who is talking, but the mozilla definition is probably as good as any; it could be anything that adds functionality to your web browser, regardless of the context.
Key Differences
Extensions tend to be automatic once installed. Plugins are instantiated in one of two ways: 1) by an <object> or <embed> tag in the HTML of a web page, or 2) because they are registered to be the handler for a mimetype which the browser doesn't support.
FireBreath
FireBreath deals with plugins. It has nothing to do with typical browser extensions, only plugins. It is a C++ framework, not a javascript framework, and it allows you to add functionality that can be used from within a web page. Typically FireBreath plugins are used from inside a <object> tag.
FireBreath post-NPAPI
As you may or may not know, Chrome has dropped support for NPAPI plugins (as of version 45) and Firefox has done so as of version 52 (excluding the version 52 Extended Support Release, which will support them for another year). FireBreath 2.0 is now being used in production by several companies and can produce "plugins" (not really plugins, but work similarly) which can work with Google Chrome and Firefox via Native Messaging via a helper extension. The main limitation is drawing; there is no way to draw directly to the browser across native messaging (well, no good way, and no way at all on platforms other than windows).
Eventually we may add support for some abstraction to draw using Canvas / WebGL over the native messaging bridge in FireBreath 2.0, but that hasn't been done yet. Frankly, I don't need it, so I haven't bothered to do it. FireBreath is an open source framework which has unfortunately not received enough support from users in the last couple of years and so the documentation is a bit outdated and there are a lot of little things which haven't been done.
The Native Messaging method relies on an Extension -- we did this primarily to confuse everyone, of course, but also because it was the only way to allow us to communicate with FireBreath plugins from the page in Google Chrome or Firefox.
*(Last updated Mar 6, 2017; Firefox 52 is scheduled to release tomorrow)
Hope that helps. See also:
Browser Plugins vs Extensions -- the difference
FireBreath 2.0 home page