"Application" was around way earlier, as shorthand for "application program" (to be distinguished from "utility program", and, possibly, "game")

For examples look at the search hits in https://archive.org/stream/1981-03-compute-magazine/Compute_....

I wouldn't call this an application, though.

"App" is completely wrong, as it was introduced by Apple for user-facing programs running on a mobile phone (if Android had been the OS popularizing this, Google would have picked the first three letters of its company name as the new name for these things, and every web site would have a banner "install our goo" :-))