Often these pistols tend to still be considered DAO, even if it isn't a strictly accurate description... But sometimes there are special names for that particular trigger mechanism... I think H&K have something like that, called the DAK or something... I may be mistaken here, on how that system works. I think a couple other big companies did something similar, using special names.
I believe you are thinking about the Heckler and Koch L.E.M. (law enforcement modification) trigger mechanism. This is a two-stage hammer-fired trigger mechanism that utilizes a bobbed hammer. This is hard to categorize as either DAO or DA/SA. It has an internal mechanism that is cocked and partially tensions the hammer when the slide cycles. It might be considered an assisted double action only trigger. The initial trigger pull is long, but smoother and lighter than the DA trigger of a DAO or DA/SA pistol, and the reset is short like a DA/SA pistol and not at all like a DAO pistol.
The DAK (Double Action Kellerman) was a SIG Sauer trigger mechanism that SIG now seems to be phasing out. This was more like a DAO trigger system with an intermediate reset point. This allowed the pistol to be fired if the shooter short-stroked the trigger after the first DA trigger pull. But the trigger pull weight was actually heavier from the intermediate reset point than it was if the trigger was allowed to fully reset.