Two clips play, one clean and one saturated, and you pick the saturated one. Both are matched in loudness, so the only clue is the saturation itself: the added harmonics, the thicker texture, the slightly softened peaks.
At level 1 the saturation is strong and easy to spot. Every level lowers the drive range, and by level 10 the effect is subtle enough that you have to listen closely to the texture of the sustained sounds to find it. Tolerance doesn't apply here: it's A or B, so the difficulty lives entirely in how light the saturation is.
Mostly degree. Saturation is gentle: it adds harmonics and thickens a sound while keeping it recognizable. Push the same process harder and it becomes audible distortion.
Because it mostly changes texture, not level or tone balance. It often reads as 'warmer' or 'denser' rather than as an effect, which is exactly why it's worth training.