A direct expansion air conditioning unit, also called a DX unit, cools indoor air using a condensed refrigerant liquid. DX air conditioning unit is the most commonly used system in homes in United States.
A split air conditioning system puts the compressor and condenser outside the building and the evaporator and fans inside the building. In a central air conditioning unit, fans push cooled air from a centrally located evaporator through ducts to the entire building. In a ductless split system, fans that are mounted on wall move the air from the evaporator into the room.
Find out more about Split Systems in this article and this infographic from energy.gov.