Air draft is the distance from the surface of the water to the highest point on a vessel, similar to the "deep draft" of a vessel which is measured from the surface of the water to the deepest part of the hull below the surface, but "air draft" is expressed as a height, not a depth.
The vessel's clearance is the distance in excess of the air draft that allows a vessel to pass safely under a bridge or obstacle such as power lines, etc. A bridge's clearance is most often noted on charts as measured from the surface of the water to the under side of the bridge at Mean Highest High Water (MHHW) which is the most restrictive clearance. The height of the tide at any time below its highest point at MHHW will then increase the clearance under the bridge.
At several bridges, such as the Gerald Desmond Bridge in Long Beach, CA, NOAA has installed an "Air Gap" measuring device that accurately measures the distance from its sensor on the bridge to the water surface and can be accessed by marine pilots and ship's masters to aid them in making real time determination of clearance.