Differences between Wikipedia, Wikimedia, MediaWiki, and wiki/el

Confused about the differences between MediaWiki, Wikimedia, Wikipedia and wiki?

Wiki
Wiki is a generic term which is used to describe a certain kind of collaborative website that can be edited by any user and/or visitor; it is not a proper noun.
 * wiki (as an adjective), "the wiki way", and the antonym un-wiki are also used to describe the community-oriented philosophy that goes with such a system (e.g. "that's not a very wiki way of doing things").
 * Wiki (with a capital 'W') is an incorrect term, although it has sometimes been used to refer to either Wikipedia or the Portland Pattern Repository (also known as WikiWikiWeb), which was the first wiki to be created.
 * wiki software and wiki engine are terms referring to pieces of software that power wiki-based websites. There are many different types of wiki software; some very simple, others with advanced features. See also: Wikipedia's entry on "wiki software".

For a more complete description, see Wikipedia's entry on "wiki".

Wikimedia
Wikimedia is the collective name for the Wikimedia movement, revolving around a group of inter-related projects, including Wikipedia, Wiktionary, Wikiquote and others, which aim to use the collaborative power of the Internet, and the wiki concept, to create and share free knowledge of all kinds.
 * The term Wikimedia servers is often used, referring to the computer hardware on which all Wikimedia projects are hosted.
 * Wikimedia Foundation is a non-profit organization headquartered in San Francisco that runs the Wikimedia projects. Wikimedia Deutschland, Wikimedia Russia etc. are the names of dozens local chapters of enthusiasts of Wikimedia projects. They are independent from the Wikimedia Foundation and the Wikimedia projects. Wikimedia, depending on the context and locale, is often incorrectly used as short name for the Wikimedia projects, or a chapter, or the Wikimedia Foundation (the latter can happen also on this wiki).
 * The Wikimedia Meta-Wiki, commonly referred to as Meta, is the wiki used to discuss issues which affect all Wikimedia projects. See also: About.
 * Meta should not be confused with MetaWiki, a search engine that is not part of the Wikimedia group of projects.

Wikipedia
Wikipedia is a Wikimedia project that is a global, free and multilingual internet encyclopedia. It is the oldest, and largest, Wikimedia project, predating the Wikimedia Foundation itself. Wikipedia is a wiki that runs on MediaWiki.

MediaWiki
MediaWiki is a particular wiki engine, that is developed for and used by Wikipedia and the other Wikimedia projects. MediaWiki is freely available for others to use (and improve), and it is in use by all sorts of projects around the world.

See also How does MediaWiki work?, Sites using MediaWiki, How to become a MediaWiki hacker.

Video

 * [//www.youtube.com/watch?v=gXD1TRGafQ0 The State of Wikipedia] on YouTube