grammar - "Over vs Above" and "Under vs below"


Is is possible to say that "Above" means "over" and "Under" means"below", but not the opposite?


According to my grammar:


Over - In a higher position (close or touching) Above - In a higher position


Under - In a lower position (close or touching) Below - In a lower position


Example:



There's a helicopter flying round above / over the school.



I would interpret this sentence as "above" meaning almost touching the school or not. And If I hear "over", the helicopter is almost touching school.


This makes me think about "over" and "on". "On" means that something is touching something, but if "over" can mean also "touch".Well, I would never use "over" to mean "touching something", I would use "on" instead.




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