A template is a type of Joomla! extension that changes the way your site looks.

There are two types of templates used by the Joomla! CMS: Front-end Templates and Back-end Templates. The Front-end Template controls the way your website is presented to the user viewing the website's content. The Back-end Template controls the way your website's administrative tasks are presented for controlling management functions by a Joomla! Administrator. These would include common tasks such as: user, menu, article, category, module, component, plugin and template management.

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

Template style is a feature introduced in Joomla 2.5 that allows users to assign different template styles to individual menu items. By default, Joomla! assigns a template style to all menu items upon installation. A yellow star indicates the default template style in use. A default template style can be partially or completely overridden by assigning different template styles to the desired menu items in order to obtain a different look for their respective pages.

A template style can be assigned to menu items one of two ways.

Template manager Extensions ? Template Manager

Editing a menu item under Menus ? Menu Name ? Menu item

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