The purpose of any heat pump is to move heat from some material at lower temperature to another material at higher temperature. The “material” that supplies the heat (e.g., the “source”) can be just about anything from which heat can be reliably and repeatedly extracted through a heat exchanger to an evaporating (or absorbing) refrigerant.
The most common sources of low temperature heat are outdoor air and water. The most common type of heat pump for space heating and cooling extracts heat from outdoor air and is thus called an air-source heat pump. Heat pumps that extract heat from water appropriately are called water-source heat pumps. When the water comes from a well, pond, lake or passes through tubing buried in the earth, more specific names include geothermal, ground-source or even earth-linked heat pumps.