The arduino sends pulses to the servo motor much like sending them to an ESC. The pulses have a different meaning. The pulses describe a spot to go to. Within the servo there is a feedback mechanism that counts shadows or turns a variable resistor. The servo circuit board then moves the servo to that spot. It knows when it has reached the spot when a certain number of shadows have past or when the resistance reaches a certain value. The arduino has to keep sending the same position over and over again to hold the motor in a current spot. Short pulses go one direction, long pulses the opposite direction, medium pulse widths go to the middle. Middle is typically 1.5 milli seconds.
One way to distinguish the center tap (common wire) from a coil-end wire is by measuring the resistance. Resistance between common wire and coil-end wire is always half of the resistance between coil-end wires. This is because there is twice the length of coil between the ends and only half from center (common wire) to the end. A quick way to determine if the stepper motor is working is to short circuit every two pairs and try turning the shaft. Whenever a higher than normal resistance is felt, it indicates that the circuit to the particular winding is closed and that the phase is working.
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