The difference between air displacement and system liquid is in the way the pipetting is performed. Basically when having system liquid, the aspiration and dispense motion is created by moving a column of fluid (often water) through the tubing with a pump. An airgap between the system liquid and the aspirated fluid makes sure that the system fluid will not be contaminated. Off course the system fluid does not travel through the tip.
Air displacement does exactly the same, but instead of moving system fluid, it moves air. The upside of air displacement is that you will need a lot less tubing in the system, it does not require any additional fluids to be filled and maintained and so on. Especially in Life Sciences the use of air displacement over system fluid gives advantages.
Some low volume dispensing techniques, such as the BioNex Nanodrop, use pressurized system liquid. The advantage of using pressurized system liquid is an increased accuracy in the dispense enabling the system to dispense volumes of 100 nl very accurate. The airgap ass mentioned above will then also play a role in the accuracy of the dispense.