It seems to me like app has a specific meaning (to me, and to @cweiske, at least) while application does not. My suggestion would be either:
- The reverse of that in the question -- make application a synonym for app
- Remove application altogether as it is not meaningful enough to be useful.
Edit: I've looked over some of the application questions, and it is always either being used as a synonym for app or else as a generic secondary, tertiary, or later tag to generically mean "program".
Yes, we know it's a program, it's a programming site.
Using the tag in the second way adds no additional information not already provided by the other tags an title, nor is it useful to search for or group questions.
I'd now advocate for my suggestion #2 -- remove it completely, and when someone starts to type "application" in the tag box, it will suggest "app", and they can select that if it's their intention. If they really mean "this is a program" -- well, that's every question on the site.