KindlePDFviewer is the name of the application that existed first, focused on Kindle devices with a (full alpha) Keyboard. A new development branch for touch-based devices got worked on eventually, and a bit after work had initial success, was renamed to "Koreader". So "KindlePDFviewer" is the ancestor of "Koreader".
Regarding the Kobo, it's both generally refering to "Koreader".
(Addendum: There's another descendant of KindlePDFviewer, "Librerator". It is oriented to devices with low-number-of-keys input, like the Kindle 4, but also works on full keyboard Kindles)