You could google for ever, and not find two similar answers to your query.
As far as I am concerned, they are one and the same, too old (limited mind, lol) to learn new tricks, I call them all programs - or even software.. But my instinct is to regard Apps as something one mainly uses on portable devices such as smartphones and tablets.
There is a side issue, right or wrong. new users today have a tendency to call the stuff downloaded from the store as an App, or even as a Metro(MS will give you an extra definition for those!). being a sarcastic sob, I still stick to the discipline of calling the Paris underground a Metro.