Is there a way to know voltage requirements?

Lots of lights use two cr123 or one 18650. There are extension tubes so you can use 3 cr123.
Thats 3, 6, or 9 volts. All work. Same light.
I had a ultrafire 502B using one 18650. Had to see what would happen so I
put in 2 16340’s and burned it out instantly.
How do they operate the same at different voltages?
I would guess a voltage regulator but is there a way to know?
Is 3 volts a “standard”?
I have a couple of modules I want to build but not sure what they were in originally.
I can use 3V to be safe but would be nice to use more battery power/battery combination
if possibly.

The closer the battery voltage is to the led voltage, the more efficient a driver will be. Either a bit over the emitter voltage (Vf) with a buck driver or a bit under Vf with a boost driver. A buck driver will transform most of the excess battery voltage into current and so will draw less current until the battery V equals Vf then will go direct drive(battery supply current = led current) until fully depleted. A boost driver will draw more and more current from the battery to maintain Vf until the battery is depleted. Linear drivers(supply current = led current) like 7135 ones convert excess battery voltage to waste heat but are very efficient once battery voltage is close to Vf. Hope this helps.