An asylum seeker is someone who is seeking international protection but whose claim for refugee status has not yet been determined.
A refugee is someone who has been recognised under the 1951 Convention relating to the status of refugees to be a refugee.
A migrant is a person who moves from one place to another, especially in order to find work or better living conditions. People can move within a country (migrant) or to another country (immigrant).
There are a number of organisations that offer support to refugees and asylum seekers, click on the view all services button for their details.