I don't think this has been settled, so I'm not daring to modify the text, but I think Wiki the proper noun should refer to a page on the World Wide Web, while wiki the common noun refers to wikis not accessible from the Internet. That's how I explained the difference between Web and web in that article, anyway. <>< tbc
Could be, but it would be news to me. --LMS
Somebody rewrote the text of this article pretty radically, on the premise that "WikiWiki" straightforwardly means Ward's Wiki, which, in my idiolect anyway, it doesn't always and indeed rarely does. But I'm not surprised that some people think it does mean that or should mean that. If someone with more experience on wikis insists that "Wiki" capitalized is usually understood to mean "Ward's Wiki," that should be in the article (it already is, I guess).
More generally, I think this article needs another huge rewrite. The changes I made were made very quickly. Wiki the software, wiki the culture, the history of wiki, etc., there are many topics that need to be covered here. --LMS