To me, "app" was just short for "application", and it usually implied something more than a program. A program was more of an individual binary and its data files. An application could be a suite of programs; basically, it was a superset of "program" that could include multiple binaries acting toward a common purpose.

An "App" (mobile-style) is a new word. It implies (again, to me) a sandboxed program with a simplified, single-window, full-screen UI.

The same 3 letters (app) have been used my entire life to refer to computer programs, but the connotation has shifted a lot.

It seems pretty constant to me. It has always meant a user-facing program that's largely self-contained. It's not synonymous with "program," but since this story is about converting stuff for the Windows Store, I think it's being used correctly here.

But outside of the Apple world program was most commonly used. It took the rise of the iPhone for app to displace program.

This makes sense. The tight knit NeXT community used the "app" meme regularly staring at least in 1990 if not sooner.