Atari's GEM/TOS also had applications, abbreviated as "app", in the mid-80s. I don't know where people got the idea that "app" is something recent, but I've started seeing people say it in a few places lately. It's not true at all, we definitely had apps in the 80s.
I think those people are saying -- reasonably -- that the word app is recent in the mainstream popular language, not that it was never ever used by anyone until the iPhone.
Windows called them programs (until recently), and Android & iOS call them apps, so it's likely that most people have only started hearing the term in the last 10 years.
I remember hearing the Windows control panel functions referred to as applets 20 years ago or so. Likewise, java programs embedded into a web page were also called applets.
Is applet but a diminution of application, or of app?
Weren't .prgs the actual "foreground"-programs while .apps were the small helper tools that ran in the background and stayed resident even if not in focus? I distantly remember some apps getting a spot in the menu bar...
(It's been ages since I touched that system, good times, though.)