Actually, the difference between App and Application goes back way before the iPhone. Put simply, an App is a small program that is designed to perform a limited amount of functions. An application is a larger program designed to perform many functions. The MS Office apps on mobile devices fit this definition because they have a subset of the functionality present in the full applications. This definition has been in use (to my knowledge) since the early days of Java, which was used to write a lot of simple apps for specific functions.
That doesn't mean that the OS should really distinguish between them though. At least on an interface level (on a lower level, it often does need to, maybe it needs to spin up a runtime). All the user cares about is that he or she runs the given app or application and it does what he or she wants it to do.