Why battery voltage is lower than system/alternator voltage
This is more of an Electrical Engineering question than Aviation, indeed the exact same thing can be asked about any automobile.
Both of the figures that you quote are 'nominal': The battery cannot be expected to put out a much higher voltage than 12v, so in reality, all systems will work fine down to about 10volts or so, though 'normal' voltage will be 12.5v for a reasonably new, modern battery in good condition.
Conversely, the battery itself requires a significantly higher voltage to charge itself, so the alternator needs to put out 13 to 14 volts, which gets rounded off to 14v for simplicity when talking &quot;in general&quot;.
Nearly forgot - for some heavy duty systems, a 12v system is insufficient, so the battery is simply doubled up, so 12v nominal becomes 24 volt, etc., but with the same tolerances.