Tukey-Kramer or Nemenyi following Friedman

I previously asked a question here after discovering an option by MATLAB to run Tukey-Kramer for multiple comparison multcompare following Friedman test and many agreed that it is wrong, instead, it can be Nemenyi, here: R package for posthoc following Friedman and Kruskal Wallis

In the package it says that Tukey-Kramer (Nemenyi). So the question here is, are Tukey-Kramer and Nemenyi are the same test?

Secondly, I contacted MATLAB following this issue; and here's the reply:

"The book "Nonparametric Statistical Methods" by Hollander and Wolfe shows an example with the Tukey-Kramer or honestly significant difference option. This is on page 51 of the book published in 1973. This is the default choice in the 'multcompare' function in MATLAB"

So another question here is which one is correct? Can I use the Tukey-Kramer following Friedman as suggested by MATLAB?

In the package it says that Tukey-Kramer (Nemenyi). So the question here is, are Tukey-Kramer and Nemenyi are the same test?

I read the package description. In the R package, it looks like that both are the same test. The Nemenyi's test is also referred to as the Nemenyi–Damico–Wolfe–Dunn test. In addition, several other sites and scientific articles use the Tukey-Krammer as a synonym for the Nemenyi. However, the Wikipedia describes the Tukey-Kramer test as the Tukey-HSD test (thus, being not the same to the Nemenyi).

I believe that they are the same test and you can properly use it. However, I'm not 100% sure of it.

Can I use the Tukey-Kramer following Friedman as suggested by MATLAB?

The Nemenyi's test is the correct multiple-comparison post-hoc test for the Friedman's test. It is equivalent on using the Tukey HSD test as post-hoc for the ANOVA. If the Nemenyi's and the Tukey-Kramer's are the same, then you can use it :)

I higly recommend you to use R posthoc.friedman.nemenyi.test instead of MATLAB on this case, since we don't now if both tests are really the same.