When Dia-Compe came out with the first 1-1/8" threadless headset, they called it the "Aheadset" (tm). As it took over the industry, mostly for ease-of-manufacture reasons, (yes, I'm aware that there are "lighter, stiffer, better" reasons to prefer it, but the "only make (or buy) one fork and have the shops cut them to length" argument was the standard-changer,) there was a period where bike manufacturers called their 1-1/8" threadless fork / headsets "ahead-style", so that they could have the new hotness without having to buy a Dia-Compe headset.

TL;DR: It's 1990s marketing-speak for "1-1/8" threadless headset."

--Shannon