//'App' is definitely a better term than 'application' or 'program' from a UI perspective if more people can so easily understand it, but I don't understand why or how this happened. They're the same thing! It's strange

I think it's a change in perspective. A 'program' is how a programmer would describe what he codes. An app, is what it should look like to someone who is interested in just using it.

Since those using "an app" should outnumber those who wrote "the program", it is better if it's called an app. It's like how the term 'bacon' is better suited than 'pig's belly'.