I probably said the burst was the most important rating
For most of the use a battery sees in Airsoft, it'll not be getting too stressed for so long that it can't recover so the burst rating is the most useful - if it is accurate of course.
I've found that the ratings on Nuprol batteries aren't particularly useful, usually overestimated by a decent margin whereas the Turnigy ones are generally pretty good.
The current in the wire creates the magnetic field, not the voltage.
The current moves due to the voltage so you could say it's indirectly responsible but it is the current that actually creates the magnetic field around the wire.
This is also why the magnetic field weakens as the motor gets faster, which has a range of useful side-effects for Airsoft.
When the coils pass by the static magnets, they act like a generator producing Back-EMF (reverse voltage).
The power used by the motor is the supply voltage minus the reverse voltage times the current. So when the motor speeds up, the reverse voltage closes in on the supply voltage and lowers the current use.
There will always be a load applied in an Airsoft gearbox so it'll tend towards a certain figure but on full-auto, it can reach a fairly steady state.
In terms of voltage drops during load, it's complex and varies greatly between different chemistries and various other factors.
I can't say I've memorised all characteristics of all batteries in all situations 🤣but I do have a rough understanding of some of the effects.
The power capability of a battery pack is dependent on its voltage and impedence - which is kinda like resistance except that it changes based on 'stuff' (you can quote me on that) due to chemistry and other things.
The impedence of a pack tends to rise as current flows, if the pack is rated for a low discharge (C - which is not coulombs but a battery specific symbol) and a higher load is applied then the impedence will rise even faster, causing a voltage drop.
Interesting, the flow of current will heat up the pack which can actually improve the capacity. On a cold day, using your gun in longer bursts (eg 3x10 second bursts) can make the battery last longer than a similar number of shots fired more intermittently (eg 10x3 second bursts).
To answer the OP's question, think of it like this:
The voltage sets the maximum speed the gun can achieve
The C rating (or more accurately, the total pack discharge) is how close to that speed you actually get.
If your gun needs a burst of 40A on startup and 30A for continuous full-auto then having a battery that can only supply 20A will limit your performance all round.
In the same setup, having a battery that can provide 30A will give you better (but still sub-optimal) performance on semi and will allow full-auto to perform at full speed.
Having a battery that can provide more than 40A will allow everything to operate as fast as it 'wants' to but without stressing the battery.
The higher the number, the less stress the battery will get and the longer it will last, in terms of charge/discharge cycles.
I know I've rambled on a bit so feel free to ask any questions and if I've gotten anything wrong, please do let me know.
There's only one thing more fun than geeking out and that's finding someone else with more knowledge 😃