In Joomla! a Category is a collection of Articles. In Joomla! a website might have Categories called "Animals" and "Plants". Within the "Animals" Category, the website might have Sub Categories such as "Birds" and "Mammals". Within the "Birds" Category, the website might have Articles such as "Parrots" and "Sparrows".

The example above could be expanded even more with specific articles on different species of Parrots and Sparrows. Start with using an "Animal" Top Category. Placing the Sub Categories "Birds" and "Mammals" are under the Animal category, and then a "Parrots" and "Sparrows" Sub Category under the "Birds" Sub Category as shown.

Animals
Birds
Parrots
Sparrows
Mammals

Now you can create multiple articles in the Parrot and Sparrow Categories.

Categories are maintained using the Category Manager which can be reached in the Administrator (Back-end) by clicking on the Content menu, then the Category Manager menu item.

Modules are lightweight and flexible extensions used for page rendering. These modules are often “boxes” arranged around a component on a typical page. A well-known example is the login module. Modules are assigned per menu item, so you can decide to show or hide (for example) the login module depending on which page (menu item) the user is currently on. Some modules are linked to components: the “latest news” module, for example, links to the content component (com_content) and displays links to the newest content items. However, modules do not need to be linked to components; they don't even need to be linked to anything and can be just static HTML or text.

Modules are managed in the Joomla! Administrator view by the Module Manager.

Joomla default modules:

• Archived Articles?
• Articles – Newsflash
• Articles – Related Articles
• Articles – Categories
• Articles Category
• Banners?
• Breadcrumbs
• Custom HTML
• Random Image
• Search?
• Statistics
• Syndication Feeds
• Feed Display
• Footer?
• Language Switcher
• Latest News
• Latest Users
• Login?
• Menu?
• Most Read Content
• Weblinks
• Who’s Online
• Wrapper

Reference: http://docs.joomla.org/Glossary