I checked out the link, & yes there the shape doesn't change. But, I already mentioned that if there are outliers present in the data, then both standardization & Normalization works in differnet way, as they are very sensitive to outliers.

If you see the Histogram of the data in that example, then you will notice that there is a huge difference in the value counts of the quantities, and there are outliers, that is why the shape is not changed to completely Normal Distribution.

The point is Standardization converts the data distribution to the standard normal if it is nearly normal distribtuion, & if not, then Standardization tries to allign data into normal distribution.

Anyhow, if there are outliers then it is not possible.

I hope now it is clear.