For example, the gazelle doesn't want to leave the watering hole when the lion shows up, it has simply had it's options limited to "run like hell or become an appetizer" or "try and hold your ground and possibly, even probably become an appetizer". It chooses run like hell because that is the safest bet, but its desire to drink has not been fulfilled and it gives up it's desire for safety.
I guarantee it isn't taking a sip of water thinking "You know what I really want? I want to have to run my mother ****ing ass off in order to save my life. That'd be awesome right now. I hope a lion shows up. I'd feel stupid if I did it simply because I wanted to."
When it decides to leave the watering hole without any threats being present, due to the fact that the watering hole no longer suited it's needs, then it can never be classified as fleeing. In those cases, it's just moving on.
Living where you want to live is "moving on". Fleeing is "running like hell".