It's because generally Grizzly/Polar bears will only charge humans if they see them as a threat to their cubs/food.
But black bears however will stalk and charge you because they are hungry, but since humans are not ideal bear food, the bear attacking will likely be weak/starving/wounded, which makes them more easily scared if you attack them back in self-defense.
I remember hearing about a bear charging a half dozen or so hunters with large calibre rifles and it killed 2 of them despite being shot something like 50 times with high calibre rifles.
This is wrong. If you run from a bear you just can't run straight. You're best bet is to change directions relatively often because it's crazy difficult for them to turn on a dime like we can. If a smaller 200-300 pound bear chases after you though, you're probably ******
Gator's won't run after you, so it doesn't really matter. They're ambush predators. If they don't get you during the initial lunge/attack, then you're good. They won't run after you.
Fellow Floridian here. There's a gator that lives in a pond/stream between the university and the parking lot. It's pretty cool.
Animals run away when they are confused. Bear pepper spray causes the membranes of the eyes, nose and lungs of a bear to swell and the result is a nearly total, yet temporary, loss of sight and severe restriction of breathing. To be effective, bear spray has to hit the eyes and nose of the bear. Most times, bears that are sprayed leave the area allowing you time to recede.
The easiest way to tell them apart is to climb a tree.
If the bear climbs up after you, its a black bear.
If the bear shakes the tree until you fall out, its a grizzly.