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'LS' stands for Los Santos, which includes the the southern part of the map up to the peaks at the Observatory and the 'Vinewood' sign. Everything north of that is 'Blaine County'
The map as a whole lies in the fictive state of 'San Andreas'. So 'SA' would be the correct name in this case.

One question, why did the police drag out these massive concrete barriers onto the sand for a plane crash? surely a small wooden barrier would suffice

Not sure a massive crane next to the runway would pass the safety standards for an airport.