Anecdote: back in 2004, a friend brought home a cheap digital audio player from her vacation to China. IIRC, it said on the front panel that it could play back MP3, MP4, and MP5.
The same capacity corresponds to different mAh at different voltages, maybe they are playing games with that.
Also, it's not the voltage, but over-current that reduces overall produced energy.
Typically the mAh is listed at some standard discharge rate, unless the cell is specifically advertised as a high-current draw cell. But either way an honest supplier will provide the draw/capacity table for you, rather than cherry pick the best one.
-2600mAh battery (9Wh)
-500 lumen light intensity
-5W LED
-4h battery life at constant illumination setting and this is the shortest time listed.
I now know that the battery is much smaller (6Wh) and 500lm is believable for a 5W LED but it's most certainly not this bright at any appreciable duty cycle. During those 4h it has to be pulling 1.5W at most.
It's funny how most of those parameters are not false per se, but at the same time create a false image of the device's capabilities.
It was advertised as having a 2600mAh battery, but when I opened it up, inside there was a 1700mAh cell. Also no sign of purported weatherproofing, as the lens was not even glued in.
I have a 2000mAh cell in the same form factor (approximately 500Wh/l, so believable) on its way from China, which makes me wonder how did they come up with that 2600mAh figure.