Not surprisingly, given that Steve Jobs said the iPhone "runs OS X" and "these are real desktop applications", many immediately thought that the iPhone was able to run Mac OS X desktop applications like Skype and Photoshop. However, the rather sparse original iPhone technical specifications page on the Apple website noted that the iPhone does in fact run "OS X" as Jobs proclaimed during the keynote, but it does not run Mac OS X.
Essentially, the iPhone runs a scaled down version of Mac OS X optimized for a handheld device -- although Steve Jobs was insistent that it runs "real OS X" (Specifically, crashlogs indicate that the original iPhone ran "OS X 1.0" build number 1A543a.) -- but no iPhone models can run Mac OS X applications regardless. On March 17, 2009, upon unveiling a developer's preview of the third version of the operating system, Apple started referring to it as the "iPhone OS" and on June 7, 2010, the company again changed the name to just "iOS".