What's the difference between a headset, and an aheadset? I'm baffled.
The real difference is between a threaded headset and an unthreaded i.e. Aheadset. The traditional threaded headset sets the preloading of the bearings by means of a large nut on the steering tube threaded section which protrudes above the upper section of the headset. By tightening this on the thread,the steering tube is drawn up and the bearings set to the correct load. This type is used with a "Quill" stem which can be adjusted up and down to achieve the correct height.
The un-threaded headset has a steering tube with no threads. Pre-loading of the bearings is done by means of a "Star-fangled washer" which is lodged inside the steering tube. A threaded cap with a long screw screws into this washer and the cap rests on a spacer set a few mills higher than the steering tube. This is tightened, drawing the top and bottom bearings of the Headset together and when the correct pre-load is reached, the two pinch bolts of the stem are tightened which locks the steering tube in that position.
The Quill stem has the advantage of being more easily adjustable for height but tends to be heavier than the Ahead.