As Thataway said, a starting battery and deep discharge (house) battery should not be charged in parallel (both at the same time). So, I assume this question relates to two of the same batteries in parallel. If there is a slight difference in voltage between the two, power will flow from the battery with the higher voltage to the one with the lower until they are the same, even when not charging. So, when you start charging the voltages should be approximately the same. If the batteries are the same they will charge at the same rate and be full at the same time. The charger will sense when the max voltage is reached and shut down. With lead acid batteries a charger will then go into a float mode and apply a small current at the max voltage to maintain the max. This will also help equalize any slight differences between the batteries.
Lithium batteries however, are different. They have an internal BMS (battery management system) that shuts charging down when the internal voltage reaches a certain value. If you have two lithium batteries in parallel and the voltage shut-off for the charger is higher than the BMS shutoff then it will keep charging the other battery that is at a lower voltage. However, if the voltage shut-off in the charger is lower or equal to the one in the BMS the charger will shut off before the second battery is fully charged. You will then have to rely on the "voltage balancing" between the two batteries to equalize the charge.