Microsoft have been calling discrete computer programs "applications" since at least the Windows 95 era, when Program Manager was replaced with the start menu. They've been inconsistently kinda-sorta doing so since even Windows 3.x, maybe even more, but nobody was closely paying attention back then.

It didn't become the current situation of monkey-see-monkey-do until Apple started using the terminology heavily with the iPhone, as you have observed. But they actually cribbed it from good old M$, much as they've cribbed basically everything else they've done in the modern era from someone else and simply painted it glossy white.