Actually, I see the OPs point - if you put the same salary in the "Tax Comparison" and then in "Witholding tax" - Withholding tax is MUCH less. So it would appear that Withholding tax DOESN'T include the Commune tax, just federal and cantonal.
I have searched the forum for an answer to this question before anybody tells me to do this

- this actual point does not seem to be addressed, although I may have missed something as some of the threads are very long and often digress.