I think there is association between DSC & ETC, along with ETC behavior changes in different TR modes.
Here's a bit from tech docs describing the difference & relations with the two, although I get a little lost in parts in the explanation lol, it seems turning off DSC also disables the engine torque control part of the TC, so I'd guess the TC wheel spin control remains which would vary in behavior depending on TR mode. But then it's never fully off-off
DSC
DSC uses the brakes and powertrain torque control to help maintain the lateral stability of the vehicle. While the ignition is
on the DSC function is permanently enabled unless selected off by the DSC switch. Even if DSC is deselected, driving
manoeuvres with extreme yaw or lateral acceleration may trigger DSC activity to assist vehicle stability.
DSC enhances driving safety in abrupt manoeuvres and in understeer or oversteer situations which may occur in a bend.
The ABS module monitors the yaw rate and lateral acceleration of the vehicle, and the steering input, then selectively
applies individual brakes and signals for powertrain torque adjustments to reduce understeer or oversteer.
In general: in an understeering situation, the inner wheels are braked to counteract the yaw movement towards the outer
edge of the bend; in an oversteering situation, the outer wheels are braked to prevent the rear end of the vehicle from
pushing towards the outer edge of the bend.
The ABS module monitors the tracking stability of the vehicle using inputs from the wheel speed sensors, the steering
angle sensor and the yaw rate and lateral acceleration sensor. The tracking stability is compared with stored target data
and, whenever the tracking stability deviates from the target data, the ABS module intervenes by applying the appropriate
brakes. On vehicles with an automatic transmission, when the DSC function is active, the ABS module also signals the
Transmission Control Module (TCM) to prevent gear shifts. If necessary, the ABS module also signals:
- The ECM, to reduce engine torque.
- The transfer box control module, to adjust the locking torque of the center differential.
- The rear differential control module, to adjust the locking torque of the rear differential.
The DSC function overrides the differential locking torque requests from the terrain response system.
ETC
ETC attempts to optimize forward traction by reducing engine torque or braking a spinning wheel until it regains grip.
ETC is activated if an individual wheel speed is above that of the vehicle reference speed (positive slip) and the brake
pedal is not pressed. The spinning wheel is braked, allowing the excess torque to be transmitted to the non spinning
wheels through the drive line. If necessary, the ABS module also sends a high speed CAN bus message to the ECM to
request a reduction in engine torque. Torque reduction requests are for either a slow or fast response: a slow response
requests a reduction of throttle angle (4.0L and 4.4L only); a fast response requests an ignition cut-off (4.0L and 4.4L) or a
fuel cut-off (2.7L Diesel).
When the DSC function is selected off with the DSC switch, the engine torque reduction feature is disabled.
On vehicles with an automatic transmission, when the ETC function is active the ABS module also signals the TCM to
prevent gear shifts.