Cag,
The pump is not being powered by the thin wires.. Your pump is connected to constant AC power from the Breaker..
The thin wires are being used as an external control voltage.. Depending on which thin wires have the 120 Volts AC, tells the pump to run at a set speed. In your case you have two wires, so you can only have two speeds... If you had more relays, you could select more speeds.
Notice the Yellow and White wires on the Pump/Filter relay.. They are connected to the load side of the relay, so the Cell's power center only gets AC power when the relay is closed.. Which would be AUTO, Pool or Spa modes.
If you are happy with what you have, there is no reason to change it.
Thanks,
Jim R.