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 Content, 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://extensions.joomla.org/ and a number of other web sites. See also Modules.
Plugins and mambots are the same thing. Plugin is the term used in 1.5 while mambot is used in 1.0.
A plugin or 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, e.g. WYSIWYG editors, but there are many other mambots available for specific tasks. Some 3rd Party developer components have their own mambots which need to be installed in order to make the component work properly. In Joomla! 1.5 mambots will be renamed plugins.
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 by assigning them to positions and pages through the module manager in the administrative interface. Modules are installed 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. Many are freely available at http://forge.joomla.org/ for download.
In addition, some 3rd party components, modules and mambots themselves have plugins.