The small wire connects the voltage regulator to the alternator's field terminal. It sends a low-power signal to the alternator to control the field current and, thus, the alternator's output voltage.
Sense Terminal Wire
The sense wire connects the voltage regulator to the alternator's output terminal. It provides the voltage regulator with feedback information about the alternator's output voltage, so the voltage regulator can adjust the field current as necessary to maintain the desired output voltage.