No. If you buy several variants of soap, the discount will still apply provided they are all of the same size.
For example, the first discount bracket for the small soap is 11 bars. You can buy 11 bars of small soap, regardless of variant, and still get them at discount.
Meaning, you do not need to buy 11 bars of Olive Cleanse, 11 bars of Papaya Turmeric, and 11 bars of Carrot. You can buy 5 bars of Olive Cleanse, 3 bars of Papaya Turmeric, and 3 bars of carrot, and you will get all of them at discount.
The same principle applies to the big soap. However, please note that the first discount bracket for the big soap is 21 bars.