It does not matter which end was reversed. The effect is the same. Both cars had reverse polarity applied to their electrical systems. If you are lucky, one of the cable clamps was making less than ideal contact, and that would have limited current flow through the cables. That would explain the minor smoking. Also, the weak battery would have a hard time overcoming your strong battery, so your car is the least likely to have suffered any damage. If all of the jumper cable connections would have made perfect contact, there would have been nothing to limit current flow, and the cables would have gotten red hot and melted.
The damage is more likely to occur to the car with the weak battery, and that is most commonly going to be blown fuses. Computer modules have diodes between their 12 volt power supply wires and their ground wires. Diodes are one-way valves for electrical current flow. In this application they are placed in the circuits backward so they are normally turned off and no current flows through them. When you connect the jumper cables backward, or worse yet, connect the battery backward, that puts the diodes in the circuit "forward biased", meaning turned on. Now they will act like a dead short. That causes the fuses to blow, thereby protecting the rest of the circuitry. Very often you only need to replace the blown fuses once the polarity issue is resolved.
Thursday, October 6th, 2016 AT 2:41 PM