The AWC controls the power delivery and is always on in some form, ASC uses the ABS system and power cut to keep the car stable. Pressing your AWC button once disables only the power cut. Holding it turns off the stability control completely, so you can do power slides without intervention from the ABS at all.
To turn it back on just simply hit the button again or when you restart the car it is automatically re-engaged.
Unless you’re at the track I would keep your cars all wheel drive system engaged. You can never turn everything completly off anyway you can merely tone the traction control systems down so you can throw the car around a bit.