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Is Dunn-Sidak approach in multcompare identical to so-called Dunn's test?

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These two articles recommend Dunn's test as non-parametric post hoc multiple comparison test following Kruskal-Wallis test.
How the Dunn method for nonparametric comparisons works
Dunn's test
MATLAB's multcompare ( offers a few choicese for post hoc tests, including 'dunn-sidak'.
The name suggests that 'dunn-sidak' is Dunn's test mentioned above, but the description here says that it uses t distribution, so I thought that it is unlikely that this approach is used for non-paramatric data.
Is so-called Dunn's test identical to Dunn & Sidák’s Approach used by multcompare?
If not, is there a way to run Dunn's test with MATLAB? Perhaps, I need to use R (it has a package dunn.test) or Python instead?

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