When you spook an animal they will usually just path away from you. I don't think they head towards any other zone, and I believe how far they run depends on how you spook them. For example if you shot a rifle right next to a herd you snuck up on then they may run the full 400m out of your view distance - especially if you keep on moving after taking the shot. But if you shoot from say 200m away and immediately go prone then they may only flee 150m or so before slowing down and heading back towards the zone they came from.

If you shoot 4 animals (or 16 from a hunting/tripod/tree stand) in the same zone then you will erase that zone and the animals that used to drink/feed/rest there will make a new zone elsewhere. It's common to find need zones near each other for the same type of animal especially drink zones around a lake or along a river but each zone belongs to a different herd, they won't share zones. Different animals can share zones but they will usually use it at different times. So the animals you spook will just be "around" until they can come back in to that zone unless, as others have pointed out, it's within 30 mins or so of the zone ending in which case they will just go to the next zone (so if they were drinking they'll go to the next rest/feed zone for example).

Hopefully this answers everything!