If there was smoke, something zorched. ( or there is a pending coolant leak. )

12.45 V is pretty low.

When using battery voltage to determine state of charge, the battery must sit for 4 - 8 hours for the surface charge ( temp high voltage ) to dissipate. A round about way would be to run lights for 5 min then let the battery sit for 15 min and retest.

I'd say make sure the battery is fully charged then test from there as driving 20 miles isn't enough to recharge a deep discharged battery.

Lead acid battery state of charge after it has been sitting for a while. This does not test capacity of the battery. As a battery ages the " Gas tank" gets smaller, you can have a full tank but it may have shrunken to a gallon. To check the size of the tank, a load test must be applied, some of the testers at autoparts are more volt meters than load testers.

Voltages are approximate.

12.66 V 100%
12.45 V 75%
12.20 V 50%
11.95 V 25% The battery will suffer some damage if run below this voltage.
11.70 V 0%