Many modules need a white balance that is at least approximately correct. That should be provided by the white balance module camera reference mode. color calibration then tries to set the correct white balance.
You can use your camera’s white balance by turning off color calibration, and setting white balance to as shot, as I have written above.
white balance works simply by multiplying the camera’s red, green and blue values. That is an approximation.
color calibration is also an approximation, but a more involved one: it tries to take the properties of human vision into account. You can read more here: Introducing color calibration module (formerly known as channel mixer rgb). See also Chromatic adaptation - Wikipedia and Chromatic Adaptation (you may ignore the warning you get because of the unencrypted connection, as you won’t be submitting passwords).
If for your camera the reference (D65) multipliers are wrong, color calibration will base its work on incorrect input. I believe that is the case for many Sony cameras. When that happens, you can either revert to legacy white balance, or replace the ‘reference’ values with those you measure by taking a shot of a screen calibrated to D65, as described here: darktable 4.2 user manual - color calibration.
If your reference values are correct, the two setups give pretty close results in most cases.
Natural light:
Artificial light:
