Stephen Gilbert wrote in part:
The software is not the same as the project, however. When we're famous, non-technical people will only know about Wikipedia, not the software that runs it.
The way that I understood the original "PediaWiki" proposal, the idea is that there is much Wiki software (UseModWiki, etc), but ours is the Wiki software developed for the 'Pedia. Someone that uses it for some other purpose is not using it for Wikipedia anymore but is still using the 'Pedia's Wiki ware. Hence "PediaWiki".
-- Toby