Refugee
“A person 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 or, owing to such fear, is unwilling to avail himself of the protection of that country; or who, not having a nationality and being outside the country of his former habitual residence as a result of such events, is unable or, owing to such fear, is unwilling to return to it.”
The 1951 United Nations Convention Relating to the Status of Refugees
In the UK, a person is officially a refugee when they have their claim for asylum accepted by the government.
Asylum Seeker
A person who has left their country of origin and formally applied for asylum in another country but whose application has not yet been concluded.
Refused asylum seeker
A person whose asylum application has been unsuccessful and who has no other claim for protection awaiting a decision. Some refused asylum seekers voluntarily return home, others are forcibly returned and for some it is not safe or practical for them to return until conditions in their country change.
Economic migrant
Someone who has moved to another country to work. Refugees are not economic migrants.
Taken from the definitions used by the Refugee Council.