Count your blessings. It gets a lot more confusing than that.
The Wikipedia community, the people that write stuff on Wikipedia wikis, isn't the same as Wikimedia, and the various different language Wikipedia communities even divide themselves up from one another. The Wikimedia Foundation, conversely, doesn't just provide the Wikipedia wikis, but it also provides wikis for projects like Wiktionary, Wikinews, and Wikisource. It even has its own wiki, the foundation wiki, not to be confused with "Meta", the wiki that I just pointed to. The Wikimedia Foundation also allows, as aforementioned, use of its name by chapters and thematic organizations.
And of course, "wiki" is not the abbreviation for "Wikipedia". It's a word for something else.
