A refugee is someone who has been forced to flee his or her home country because of armed conflict or persecution. Syrians are a prime example.
The U.N.'s definition of refugee is someone who, "owing to a well-founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion, is outside the country of his nationality, and is unable to, or owing to such fear, is unwilling to avail himself of the protection of that country."
Migrants, however, are processed under the receiving country's immigration laws. So, ultimately, these terms have major implications for those seeking asylum and the countries being asked to grant it.

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