Doesn't make sense to me when one standard AA battery is 2,000 mAh, and 3 AAA's add up to only 2,400 mAh.
First of all, I don't know these specific lights.
However, if the mentioned 3AAA are in series(edit: had to make sure and they are), they still have 800 mAh. Of course three 800mAh AAA's have more energy than a single 2000 mAh AA, but it's a very crude mistake to add up capacities in series.
Stored energy would be 2400 mWh vs. 2880 mWh when calculated with nominal voltage. Maybe even more properly 2.4 Wh vs. 2.9 Wh as our figures are not that accurate.
I think it's really 800 mAh at just 3.6 volts for 3XAAA LSD NiMH as opposed to 2000 mAh at 1.2 volts for 1xAA LSD NiMH . I think one AA = 2.5 AAA in actual energy but could be wrong. Not sure why the runtime at 150 lumens is so much longer than 1xAA. Maybe the higher voltage has advantages within the electronics? Could be wrong on all accounts.
You are correct on all of them.
High power LED's have a forward voltage in the same range as a single lithium ion or three NiMH cells and can then be operated very economically by a simple regulation circuit(or in other economical ways). Operating on single NiMH necessitates voltage step-up, and that wastes power. It's also notable that the voltage for 3 NiMH in series is actually higher to begin with than the nominal 3.6 volts. So that's well above typical required voltage for a high power LED.
This may or may not explain it all. There might be other significant differences in circuitry as they are already fundamentally different.