The battery powers eveything and the alternator charges the battery.
If the aircraft has a 12 volt system the alternator will have to have an output of more than 12 volts to charge the battery, Usually about 14 volts under load. There is an electronic circuit to control the amount of charge.
There are different ways of displaying the load but I think the PA28s I've flown show the alternator output in amps. Others sometimes show charge and discharge. ie the "0" in the middle of the guage.
Some aircraft are 12 volt and others are 24 volt. They will need the correct alternator for the aircraft.
DO.