See if I can word this right so it may make sense and use the Tesoro Tejon as an example:
The sensitivity knob only effects the discriminators by offsetting the balance of the ground balance circuit by changing the voltage on the opamps so that lower sensitivity will move small fringe targets into the ground phase range and higher sensitivity will move them into the discriminator range.

Sensitivity does not effect the send or recieve coil power in all metal mode. So if I had a fringe target and increased decreased the sensitivity I can lose that target. Sensitivity does effect power but not in the sense of voltage going to the Rx or Tx in that sense.

Compare that to a modern macine with a VDI that has just power control ie Gain and in the field where the analog machine can do better. In an area that is littered with bits of burned debris and coal if I used Gain I could only settle the machine down by reducing it's depth so it is reacting to fewer targets.
On the Tejon I was able to drop those tiny targets and balance them out yet still be able to hit deep targets. In practice this enabled me to hear a crotal bell at 12" and a walker half dollar that my other machines were just too noisy to isolate them out.

Maybe Carl could chime in and better clarify it all?