The 1951 Refugee Convention spells out that a 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."
and a migrant as follows:
Migrants, especially economic migrants, choose to move in order to improve the future prospects of themselves and their families. Refugees have to move if they are to save their lives or preserve their freedom. They have no protection from their own state - indeed it is often their own government that is threatening to persecute them. If other countries do not let them in, and do not help them once they are in, then they may be condemning them to death - or to an intolerable life in the shadows, without sustenance and without rights.
IOM defines a migrant (and economic migrant) as follows:
Migrant - At the international level, no universally accepted definition for "migrant" exists. The term migrant was usually understood to cover all cases where the decision to migrate was taken freely by the individual concerned for reasons of "personal convenience" and without intervention of an external compelling factor; it therefore applied to persons, and family members, moving to another country or region to better their material or social conditions and improve the prospect for themselves or their family. The United Nations defines migrant as an individual who has resided in a foreign country for more than one year irrespective of the causes, voluntary or involuntary, and the means, regular or irregular, used to migrate. Under such a definition, those travelling for shorter periods as tourists and businesspersons would not be considered migrants. However, common usage includes certain kinds of shorter-term migrants, such as seasonal farm-workers who travel for short periods to work planting or harvesting farm products.
- economic migrant - A person leaving his or her habitual place of residence to settle outside his or her country of origin in order to improve his or her quality of life. This term is often loosely used to distinguish from refugees fleeing persecution, and is also similarly used to refer to persons attempting to enter a country without legal permission and/or by using asylum procedures without bona fide cause. It may equally be applied to persons leaving their country of origin for the purpose of employment
However, in today's world, the difference between a "migrant" and a "refugee" depends on the destination. The definition is now based on the economic status of the destination compared to the place of origin. Irrespective of what or where one is fleeing from, if the person flees to a poorer country, that person is a "refugee". But, if that person flees to a much better country (in economic terms), that person is a "migrant".