With the lunge you have the ball of your foot on the bench. Imagine the way a sprinter would be in the starting block on the track, kind of on the ball of the foot up on the toes. With the BSS you are resting the top of your foot flat against the bench. This position makes it harder for you to use the resting leg to "push" from.
Also, I dont have book in front of me but I think the lunge is done on the step with 1-2 risers and the BSS is shown using the wooden box (which is higher than in the pic with the lunge)
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