Aheadset is another name for threadless headset (and the horribly priced example you found is one example of aheadset). It has a fork steerer tube without threads. It is tightened by a system consisting of a star nut put inside the fork steerer tube, and a bolt that goes to the star nut to tighten the top cap. After tightening it with this system, the stem that clamps around the steerer tube is tightened and the star nut bolt no longer has any structural role.
In contrast, a threaded headset has a fork steerer tube with threads and the headset is tightened via those external steerer tube threads. You need a huge headset spanner to do the tightening, which is annoying since there's no other use for such a huge tool. In contrast, threadless headset (aheadset) can be tightened with a standard Allen wrench you can carry with you.
The stem clamping mechanism is better too. Threaded headsets have a stem that goes inside the steerer tube and a wedge holds it in place -- usually not perfectly. Since the stem is smaller than the inside of the steerer tube, it has a small gap where salty sweat and rainwater can get in, corroding the aluminum in the stem, possibly meaning you can no longer remove it or adjust its height. However, no such problems occur in threadless clamping where the stem is externally clamped around the steerer tube.
About the only drawback of aheadset / threadless headset is that handlebar height adjustment happens via spacers and usually there aren't a huge number of them. You usually can flip the stem for slightly more adjustment range, but with 20mm spacers and 6 degree stem, it's usually around 40mm total adjustment. Of course by purchasing a separate 17 degree or 35 degree stem, you can get more adjustment options.
Threaded headsets are today practically obsolete, only to be found on very cheap bikes or alternatively bikes where handlebar height adjustment needs to be very fast, such as bikes that are part of bike sharing.