You're too specific, ANY circuit will draw less current at a higher nominal voltage everything else being the same. Does not matter if AC, DC, single phase, multi phase.

As to battery rating, a marginally sized battery, when new, will age and give less ampacity. As the ampacity (sometimes shown as CA-cranking amps for starter batteries) the voltage will drop more causing more heating of wires.

As to wiring, the current rating (ampacity) is based on continuous current in free air, momentary higher amperages can be handled with no ill effects.
Enclosing the wire reduces the continuous current rating since it is no longer in free air.
This part of why a smaller wire can be used for starting and yet deal with the short term inrush current as the circuit is energized. Multiple start attempts WILL start to heat the wire.

No, I'm not an EE, many years in facilities doing wiring and 15 years working with large UPS batteries.

I did stay at a Holiday Inn Express a few times though. ;-)