You're decades late on this. "App" has been used as a shorthand way to refer to programs for a loooong time. Random example, Apple had an object oriented framework called MacApp in 1985.
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.