what is the difference between above and over;under and below?
 

Both the words above and over, are used in the sense of ‘higher than’. The main difference lies in the context they are used. The term 'over' indicates movement, whereas 'above' indicates that something is physically higher than something else.
For example, 'a chopper flew over a city' and 'a chopper is above a city' have two different meaning. 
'A chopper flew over a city' indicates that the chopper flew from one side of the city to the other side whereas ‘above the city’ indicates that the chopper was in the air higher than the city.

Below and under are  similar in meaning i.e. ‘lower than’. Below is preferred when one thing is not directly under another, while under is used when something is covered by what is over it.
Example:
The cat is under the bed.
The temperature is eight degrees below zero.
 
 
 

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Above and over - 

Both above and over function as adverbs, prepositions, and adjectives, but since there is no overlap in meaning with the adjectives, I'll only address the adverbs and prepositions here.

In its most common senses, the adverb over implies movement from one location or position to another:

Under and Below - 

Under and below both mean at a lower level and can often be used interchangeably:

In general, under is more specific and tends to indicate a direct vertical relationship of objects; below indicates merely being on a lower level, and the objects may not be vertically lined up.

In some circumstances, only under (not below) applies, to include the idea of touching, or of being covered. Eg:


On a cold night, it’s cozy to be in bed under the covers.

The roads were all under water because of the heavy rain.

On the other hand, below, not under, refers to a place or position and means “lower than”.

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