Definitions

Refugee: A refugee is someone who has had to leave his or her country and who is afraid to return there "owing to a well-founded fear of being persecuted for reasons of race, religion, nationality, membership of a particular social group or political opinion."; (1951 UN Convention Relating to the Status of Refugees)
Asylum seeker: An asylum seeker is a person who has crossed an international border and is seeking safety or protection in another country.; In the UK, an asylum seeker is a refugee who has claimed asylum and is awaiting a Home Office decision as to whether he or she can stay here.
Indefinite Leave to Remain (ILR): If the Home Office decides that the person's claim is acceptable, they will be granted Indefinite Leave to Remain. This is also known as Refugee Status.
Exceptional Leave to Remain (ELR): Until April 2003 the Home Office would grant someone ELR if they fell outside of the strict definition of a refugee, but would still be in considerable danger if they returned home, or on Human Rights grounds. This was usually granted for an initial period of 4 years, with the possibility of subsequent extension.
Humanitarian Protection: The Home Office grants Humanitarian Protection to a person who would face a real risk of death, torture or other inhuman or degrading treatment if returned to their country of origin. This should be granted for three years, although it can be granted for shorter periods.
Discretionary Leave: This can also be granted if the person does not qualify for Indefinite Leave or Humanitarian Protection, but cannot be removed for some other reason. These can include having a serious medical condition which cannot be treated in the home country, and is usually granted to unaccompanied refugee children until their 18th birthday.