All air conditioning units require some sort of access to the outside to vent heat, so it is not possible to have an air conditioner that is entirely indoors. However, central air, mini-split and portable air conditioners do not need to be exposed to air directly.
Air conditioners operate by using a refrigerant fluid to exchange heat from inside of a building to the outside. Window and wall-mounted units need to be exposed to the outside to work correctly. Central air and mini-split interior units use ducts or tubes to transfer heat to an exterior unit, so they do not need to be directly exposed to the outside. Portable air conditioners have exhaust hoses to expel heated air, so only the exhaust hose itself needs to be run to a window or other opening.