I think ‘jump-start’ means ‘to help [jolt it] back to life’ and ‘kick start’ (as in the olden way of starting motorbikes) is ‘to [use] force to start’.

BTW. This You revive a dead battery
by jolting it to life with a jumper cable
is odd. Usually a ‘dead battery’ means “dead” and no longer usable. But a “flat” battery means “weak” and can be charged up to good condition. A jumper cable is not very useful as we all know a battery has 2 different terminals and need 2 cables to connect to another source of power.