I’ve no idea about vaping but if you put a high load on a battery the voltage will drop due to the internal resistance.
So Say you start off with a freshly charged 8.4V battery, and connect that to a 1ohm coil. You would get 8.4/1=8.4 amps, and therefore 70.5W. But in reality the voltage of the battery will drop to say 5V when trying to produce that much current, so only 25W (i.e. a massive difference). Hence why you can probably buy a battery that claims to deliver so many watts, because what it’s really saying is it can deliver so much current before the voltage drops.
I guess in an effort to standardize this for the experiment they’ve hooked the coil upto a power supply so can say that “at 5V the coil produces formaldehyde”. Which is a different statement to “connected to a 5V battery the coil produces formaldehyde”.