Hi,
...and a long(winded) answer is:
You would need to do the "legwork" of reading about how linear regulators work. These questions are quite basic and usually covered in most regulator tutorials/lectures.
Short-circuit protection means it limits the heat generated by lowering the output voltage as the excess current rises. Ugly and horrible but effective. Like trying to tame a wild horse but it keeps straining at the noose. Or, if you have a burst pipe, lowering the rate/speed of flow through it will ... basically, reduce the damage until the plumber arrives to fix it, but you haven't turned it off at the main water switch, you're just trying to stem the speed of flow.
Thermal shutdown means shutting down at a specified temperature. Not the same as short circuit protection. It will switch on and off as the temp falls below and rises above 165ºC if the fault condition is still present after the first shutdown.
"safe area protection" isn't in the datasheet I saw, a far as I can see from three readings. It sounds good to me, possibly gimmicky wording but what is it? SOA or a way of repeating that it shuts down when the junction reaches 165ºC?
The datasheet referred to seems quite clear about avoiding exceeding 125ºC junction temperatures.
Short circuit limits, shutdown turns off.