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What's the difference between District and Region? or they're synonyms?
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heywoodcIn the British use of the words, a district is a part of a town or city.

However, it can also be used for an area of countryside, or an area including both towns and countryside. It is still usually smaller than a region.
Comments  
In the British use of the words, a district is a part of a town or city.  A region is a much larger area referring to areas of a country or part of the world.
This is an excellent online dictionary 
http://www.ldoceonline.com/dictionary/region  
which will give many examples.

The words are used in often used in administration eg.
Many Indian people live in the district of south-west London.  
There are many major hospitals in the North-East Region of the UK. Here the region is given a name so North-East is capitalised.
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A district is an administrative division.

A region is a geographical area or division having definable boundaries.Its also an administrative area. So yes , they are synonyms.
 Mr Wordy's reply was promoted to an answer.