The Miss rule is the most confusing thing about Snooker ever. It's a judgement call that's just annoying.
I think it applies in the case where there is an easier alternative escape that hasn't been chosen. Thus, supposing you have a "one-cushion escape" but decide to take a safer two- or three- cushion escape, or play the one-cushion escape too soft. Obviously if you'd hit it harder it would guarantee the escape, if not leave things safe.
It doesn't apply to other fouls, usually -- most famously, I think John Higgins suffered once when O'Sullivan was in a tricky situation, snookered on all colours and trying to find the brown (or some other baulk colour). After two or three attempts called as "misses", he accidentally touched a red with his bridging hand and it was called "foul", no miss -- which annoyed Higgins rather.
If you pot the white during your attempted escape and also miss the object balls then I'm sure it would be called "miss" too. But the rule could really be tightened up. Essentially, though, the application seems to be that whenever the player is putting safety ahead of escaping the snooker easily, then it will be a miss.