A split menu is where different levels of a single menu are displayed in two or more locations on a single web page.

For example, a common requirement is for a menu of top-level items to appear at the top of the page. When one of the items is clicked the user is taken to a page where a secondary menu, say on the left of the page, shows second-level items within the scope of the top-level item.

The menus appear in separate locations on the page, but are related because one shows only top-level items while the other shows second-level items.

This idea can be extended to include menus for third-level items and beyond.

This can be implemented in Joomla using a single multi-level menu then creating more than one menu module each referring to a different level.

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

The word "core" in Joomla! pertains to the distributed files which are needed to create and administrate a Joomla CMS powered web site. These files can be downloaded from the Joomla website at http://www.joomla.org/download.html. The Joomla "core" also contains some basic functionality to get new Joomla installations working quickly and easily. Included are the user manager, article manager, weblink manager, category manager, contact manager, and menu manager. There is also a template manager with a few basic templates to power the front-end (website/user) view, a module manager with basic modules, plugin manager with basic plugins, and a few other "out of the box" extensions to extend the functionality of a basic Joomla installation. These core's extensions should not be confused with extensions which are available for downloading from the JED (Joomla! Extension Directory).

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