Addons are bits and Bobs you can add into the system to make it work in a more tailored way. You can Install these through the admin panel and are very easy to work with. Problem is many of them made are freely given away under the Open Source agreement, and in so have no official support package, so if something goes wrong, it will simply not work on your system and YOU have to fix it.

Typical extras are

• Shopping systems
• Forums
• Chat Rooms
• Galleries
• New Tool Bars
• Newsletter systems
• Poll/Voting systems
• Site Map Generators
• Calenders
• Real Estate systems
• Classified Ads systems

There are literally thousands of extras out there, take a look at the developer site on Joomla to see what i mean.

But we can do this for you, including the making of an extra bit, that is to work and do as you need. 

So what is exactly the difference between these extras? 

Sometimes it is difficult to distinguish the difference between a component, module or mambot. For example, many components use modules to display their information to the user. Please try to determine if your question is about the component itself or the module or mambot. The definitions are as follows.

From http://help.joomla.org/component/option,com_glossary/Itemid,213/

Component
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Components are Joomla!’s content elements or applications that are usually displayed in the center of the main content area of a template. This depends on the design of the template in use. Components are core elements of Joomla!’s functionality. These core elements include Banners, Contact, News Feeds, Polls and Web Links. Members of the Joomla! community produce third party Joomla! components on a continuous basis. They are freely available to download from http://developer.Joomla.org and a number of other Web sites.

Module
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Modules extend the capabilities of Joomla! giving the software new functionality. Modules are small content items that can be displayed anywhere that your template allows it to be displayed. Modules are very easy to install in the Admin Section. Joomla! modules may include: Main Menu, Top menu, Template Chooser, Polls, Newsflash, Hit Counter, etc. Members of the Joomla! Community produce Joomla! modules on a continuous basis. They are freely available on http://developer.joomla.org for download. An example of a module PHP code is <?php mosLoadModules ( ’module position’ ); ?> .

Mambot
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A Mambot is a small, task-oriented function that intercepts content before it is displayed and manipulates it in some way. Joomla provides a number of Mambots in the core distribution.  Some examples are such are WYSIWYG editors, 3rd party component and module searchers