A (computer-)application is always a program, but not all programs are applications. The number of files is generally not important for the distinction.
A program is a set of instructions telling a machine what to do. A set of instructions does not necessarily stop being a program, when it is split up across multiple files.
An application is a (computer-)program, that solves a functional user-task, e.g. it plays some music, displays some documents, lets you edit something...
There used to be a discrimination between application software and system software. The later solves technical tasks. Operation systems, device drivers, etc. are system software (Most of the time, you will need lots of system software to get an application running. But the distinction between user-tasks and technical-tasks can get quite blurry).
You can find those definitions somewhere in ISO/IEC 2382. I'd bet that there are other, possibly contradicting, definitions for specific contexts. But I doubt that there is an important distinction between an application and a program for most practical matters