There seems to be some confusion re battery capacity.
I will have a go at explaining this. This is my 3rd attempt at writing this post so hopefully it will make sense.
Note-I have used 3.7V & 7.4V to simplify matters, the voltage obviously depends on charge. Also capacity changes under different loads but we will use the rated figures.
MAH's & Wh's
First mAh's. We all use this to indicate battery capacity, which in simple terms it does. However, it is not a particularly useful measure to compare batteries across different voltages without properly understanding it. The mAh rating indicates that the battery can deliver ---mA for 1 hour at it's rated voltage.
For example- An 18650 3.7V 2000mAh battery can deliver 2000mA(2A) at 3.7V for 1 hour. It can also do 1A for 2 hours. or 4A for 1/2 hour etc
This is the- current capacity -of the battery.
To compare a 3.7V battery to a 7.4V battery we want to know what the power(watts) capacity is. This is Wh(Watt hours), you may see this on some batteries(some of my AW's have this on)
This allows us to compare the actual amount of energy stored in cells across voltages as this figure takes account of voltage.
To calculate the Wh of a battery you multiply the voltage by the Ah rating(if you have mAh, divide it by 1000 to get Ah). V x Ah = Wh
Using the same 18650 for example-3.7V 2000mAh(2Ah) battery. Multiply voltage by Ah. 3.7V X 2Ah =7.4Wh
So this 18650 has a power capacity of 7.4Wh which means it can run- 7.4W for 1 hour, or, 3.7W for 2 hours, or, 14.8W for 30mins,
Multiple batteries-
If we add multiple batteries to make a parallel pack (3.7V) we add the mAh rating of the batteries together and the voltage stays the same.
If we make a Series battery pack we add the voltage of the batteries together and the mAh rating stays the same as one battery.
Say we take 2 of those 18650 2000mAh batteries and run them in parallel. We add the mAh ratings- 2000mAh + 2000mAh. Voltage stays the same.
We get a Parallel(1S) 3.7V 4000mAh(4Ah) battery pack.
Now if we take 2 and run them in series then we add the voltage- 3.7+3.7. The mAh rating stays the same as one battery.
We get a Series(2S) 7.4V 2000mAh(2Ah) battery pack.
It now looks like we have less power in the 7.4V pack because 2000mAh is less than 4000mAh, but comparing the power capacity shows they have the same.
Using VxAh=Wh here is how it works out-
Parallel- 3.7V X 4Ah = 14.8Wh
Series- 7.4V X 2Ah = 14.8Wh
Both packs can run 14.8 Watts for 1 hour, or, 29.6W for 30mins, or, 59.2W for 15mins.
Assuming a chip (like DNA30 or SX350) to be running at 100% efficiency then it would make no difference(if the board allowed) to use either series of parallel packs from the example. They would both run the same wattage for about the same time.
Board efficiency, wiring losses, battery discharge profile, load, temperature, etc all play a role in battery life and are affected by voltage so other factors have to be considered to determine battery life and configuration. Typically 7.4V will give lower losses/longer life given the lower loads to achieve the same power as 3.7V.
Hopefully that explains something, let me know if anything is incorrect.
A little bit I found which may also help explain battery capacity-
The energy stored in a battery (or its capacity) is expressed in watt-hours (Wh). For historical reasons, the rated voltage in volts (V) and the charge in ampere-hours (Ah) are sometimes also stated. In this case, the energy stored in the battery is calculated by multiplying the voltage by the charge.
Unfortunately, there are very few areas of technology where manufacturer's data are as confusing as with battery capacity. For example, you might think that a battery specified as 12 V and 100 Ah, which therefore stores 1200 Wh of energy in nominal terms, should be able to deliver 100 A of current, or 1200 W of power, for one hour. However, you would be wrong.
As a result of the internal resistance of the battery, the available capacity falls off with rising current.