Single-Action airbrushes have a nozzle that you adjust to set the spray pattern. This means the air will pass through in this spray pattern whatever you do. To achieve a different size spray pattern with a single-action airbrush you have to stop and adjust the nozzle. You have one trigger that controls both air flow and paint flow at a non-variable rate.
Double-Action airbrushes allow more control over what is coming out of the airbrush. Air passes through when you press down on the trigger. You can control how much air feeds through by depressing the trigger to different levels. Pulling the trigger back while pushing down then starts to draw paint through, again at a variable rate. While these factors have an effect on the spray pattern, most double action airbrushes also have different needle and nozzle sizes available to further control this.
In the video below Max tells us more about the differences between Single Action and Double Action Airbrushes