Components - is expanding Joomla, which constitute a functional system and support interact with the user, components are the Joomla forums, file archives, galleries, gathering system statistics, backup, etc. Managing users, partition - is also a component, but working only in the administrative part of the site. A Adding and display materials - components working in the admin, and a public part of the site. Component search is only the public part
Modules, in contrast to the components, perform the functions of displaying any information, and in most cases do not perform any operations for adding / modifying data. Another important difference between modules of the components is the ability to copy modules. Typically, the modules are located in the left and right column with three-column layout. Examples of modules is the navigation menu, a calendar, a list of popular articles, etc.
Mambots - these are small features enable you to manipulate data before rendering their users of the site. An example of the mambot - search the text of conditional code, which he programmed and replace it with another.
In most cases, an extension for Joomla component consists of one or more modules, and a search mambot. A component which performs an action with the data (add / edit / delete) module displays the data, and mambot allows you to search according to this component.