It's about the voltage required by the DC-ATX unit.
HDPlex is a 19.5 v system. It means the adapter (the AC-DC unit) will convert whatever voltage from your wall to output 19.5 v. The DC-ATX unit will then convert this down to 12 v (and 5 & 3.3 v). Pros: this is the same voltage like vast majority of laptops, which means you can find adapter easily (at least the lower wattage ones). Asrock DeskMini also use this voltage, if I remember correctly. Cons: there will be extra heat from voltage conversion from 19.5 to 12 v. This is the reason HDplex DC-ATX unit has that big overhang heatsink.
On a 12 v system, the adapter (AC-DC unit) will convert the wall voltage to 12 v instead. The DC-ATX unit will then convert this further to 5 and 3.3 v. Pros: there will be less heat at the DC-ATX unit, as majority of voltage conversions happen in the AC-DC unit. Cons: a bit harder to find adapter.
(I'm not an expert here so perhaps
@REVOCCASES can correct me if I'm wrong)
I'm not sure about keyword.. when you search for Pico PSU or Nano PSU, check the voltage.