There are 2 plugs/ports on the SATA drive:
One for power, 15-pin (flat/black) from the power supply, plugging into the drive.
One for data, 7-pin (flat/red or ??) from the drive to the motherboard SATA port.
That is it!
Now these plugs from the PSU maybe on the same "cord" from the PSU, mine have 4 SATA plugs on one cord. Is this what you mean?
I'm confused about your "3rd cable" reference.