If the AppStore and iTunes Store apps themselves have disappeared have you checked in Settings > General > Restrictions to see that they haven't been disabled?
There is no separately downloadable AppStore app, so I've no idea what it is you were attempting to download.
Don't immediately assume it is a bug, before you have checked all user settings, especially when no one else is reporting the same "bug". If it were a bug, it is highly unlikely only you would be experiencing it.
I have the same problem. Since ios-update (6) on ipad3 the app "itunes" disappeared. Instead there are the apps Podcast and uTunes. No app synch. All other (music etc) are working. Itunes-software (11-0-1) automatic synch check box is inactive. Synching by cable (Mac Pro 10.7.5). Settings checked. ipad completly set up new. It did not help.