An asylum seeker is a person who fled from their country but is not accepted yet as refugee. refugees and asylum seekers are different.
The decision whether a person is a refugee or not is most often left to certain government agencies within the host country. This can lead to a situation where the country will see a asylum seeker neither as refugee nor as legitimate migrant. Then they will be treated as an illegal alien (a person who is not a citizen of the country) even if their life was endangered in the country they fled from.
As long as a country does not see a person as refugee, this person will not have the rights and the country will not have the obligations that the legislation of the receiving country and the Convention Relating to the Status of Refugees gives to refugees.