You can choose whatever words you want for it, but there's a difference between the targeted polished UX of "there's an app for that", and a morass of software that may or may not serve your needs that kind of sort of works together if you hold it right.

Is that true? mv isn't an application. To me, the GNU toolchain is more like an application, but the individual parts like GNU ld, GAS, ar, GCC, etc. are just programs, not applications themselves. And even then, application feels like it implies GUI, maybe?

I'd say something like GNUCash is an application, but hledger feels more like a program. Brewtarget is an application, but bc isn't.

Certainly app and application are synonyms.