(spilling as an answer to another thread)
Shortly, the only importance with Volts is that one must buy a battery compatible with the laptop.
And the only importance overall is the energy of the battery pack in mWh.
But beware that the battery world is known for overstating energy, power and charge.
Should you have to compare mWh and mAh, just multiply mAh by Volts to get mWh.
Now, if you're curious and want to make more conclusions... Some theory first
1 C(oulomb) is the electric charge of (really) many electrons ( 6 241 509 629 152 650 000).
It is a quantity of electricity, like a quantity (volume) of water.
1 A(mpere) is the current (like the flow of a river) of 1 C(oulomb) during 1 s(econd) = 1 C/s. (2 A = 2 C/s or 1 C/½s) A river may flow 1 m3/s.
1 mAh (milliAmpere × hour) is the quantity of electricity carried by 0.001 A during 1 hour.
Hence, 1 mAh = 0.001 A × 3600 sec = 3.6 C.
The quantity of electricity is not an interesting measure.
What matters in electricity to power a device is its energy.
The energy is the quantity of electricity multiplied by the difference of potential climbed (Volt).
Volts are like the height our river cascades down: energy is water mass × height × g.
Energy mW(att)h = mAh × V(olt).
A problem is that the potential (voltage) of a accumulator varies during charge/discharge.
Not much for NiCd (1.1-1.2) but more for Li-ion (3.6-4.2).
Hence, for the same current, more energy flows per mAh at 4.2V than at 3.6V or 1.2V.
mAh does not account for that.
mWh does and can be used to compare energy of batteries at or of different voltages.
Watt is not a energy, it's a power.
The power is the quantity of energy a battery is producing or able to produce per sec or per h.
That is why one must "sum up" W during 1 h to get the energy 1Wh = 1W × 1h.
A (very special or old) battery could have much energy but little power, that's be able to produce energy slowly, maybe because its internal resistance is high and current is heating it.
So much for the theory, now in practice...
Laptop battery packs are most usually made of 18650 or like Li-Ion accumulators.
The voltage of a 18650 varies from 3.6 when empty to 4.2 when full.
3×18650 are connected in series to produce 3×3.6=10.8 to 3×4,2=12.6 V.
But the battery could use 4×18650 in series, giving 14.4 to 16.8 V.
Unless there is a voltage regulator in the battery, that's all there is to it.
2 or 3 such accumulator series are connected in parallel (all + to + and - to -).
That augments the energy as well as the power by 2 or 3 but changes nothing to volts.
The total energy is the sum of (usually 6× or 9×) a single accumulator's energy.
- ──┤ ├── +
Supposing each 18650 contains N mWh energy,
- e.g. a 3 18650 series will contain 3×N mWh energy
- the e.g. 2 series 6-pack will contain 2×3×N mWh energy
Supposing each 18650 is at 4V,
- the same series will measure at. 3×4=12V.
- the same pack will also measure at e.g. 3×4=12V.
Supposing you decide each 18650 can safely flow 3A.
- the same series will also let flow 3A.
- the same pack will let flow 2×3=6A.
Regarding "life", this term is a misnomer.
End of life is when you discard something, not recharge it.
The life of a Li-ion battery may be about 3 years after which it is too rapidly discharged.
That's when the charge is kept at 100% or 0%, even if not used.
If the charge is kept between 30% and 70%, its life is about 15 years.