Profile (gravity feed or bottom feed). With a gravity feed airbrush, the paint is poured into a cup on top of the body. A bottom feed uses a hose and suction to draw the paint up into the nozzle.
Trigger action (single or dual/double). With a single-action airbrush, you press down on the trigger to get air and paint in a predetermined spray pattern. With a dual-action airbrush you press down on the trigger to engage the air and pull back on the trigger to get paint.
How paint is mixed with air (internally or externally). In an internal mix airbrush the air goes into the body of the airbrush and meets the paint inside the tool where they mix. In an external mix airbrush air and paint meet outside of the brush.