When Mochizuki's (claimed) ABC-proof came out, various media and forums, e.g. New Scientist & MathOverflow, suggested that he used “Inter-universal geometry” (for which Wikipedia has no article or redirect as of 2015-05-10), others (correctly) that his papers on “Inter-universal Teichmüller theory” are where he gives his proof. Is this a mix-up on someone’s part? What is the difference between the subjects, if any? Is “geometry” just his older terminology?
He does have papers on both, but IUG is a handwritten PDF from 2004 of what look like lecture notes, while those on IUTT (I to IV under References in Wikipedia) are cleanly type-set papers from 2012. The fourth of these includes the claim to prove ABC. Some searching on my part found various references, but left me unclear what the relevance of IUG was.