Your 12v adapter would only be able to raise the battery voltage to 12v, but to charge a car battery fully you would need to raise the voltage to 13.8v. The 16v adapter would raise the voltage too high and could cause damage.
If you do intend to use this adapter to recharge your car battery, make sure that the voltage and amperage of the charger are equal. The charging rate depends on the type of battery and power supply unit. Typically, it can safely charge a 12-volt car battery with a 1 A rate.
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charge car battery with 12v adapter