Questions about Dunn's test 
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*Authors in a paper state that they use the 'Bonferroni-Dunn test' as a post-hoc test. Is the 'Bonferroni-Dunn test' just a Dunn's test with Bonferroni adjustment or is it a different test (after searching on the internet I would say the former but who knows)?

*Can Dunn's test also be used for paired samples (ignoring the fact that pairs have a an $\alpha$ value of 1)?


Without seeing the paper it is a little unclear, but here's some possibilities:

*

*It may be that "Bonferroni-Dunn test" means a Bonferroni adjustment for multiple comparisons made to the application of Dunn's test.
Dunn's test is a post hoc pairwise comparisons test to be used after one has rejected the Kruskal-Wallis omnibus null hypothesis ($\text{H}_0\text{: }Pr(X_i > X_j) = 0.5$ for $i,j \in \{1,\dots,k\}$ and $i\ne j$, and where $k$ is the number of groups on one's data set). This test is like a pairwise rank sum test, but (1) using the ranks from the Kruskal-Wallis test when calculating the statistic for each pair being tested, and (2) using the variance estimated under the Kruskal-Wallis null (akin to the pooled variance estimate used in the post hoc pairwise t tests following rejection of the omnibus null hypothesis in a one-way ANOVA). Given that there can be up to $\frac{k^2 - k}{2}$ pairwise tests, this raises the multiple comparisons issue.

*It may be that "Bonferroni-Dunn test" means that multiple tests of some sort were performed, and Dunn's 'Bonferroni' method was used to adjust rejection decisions. (E.g., post hoc t tests following rejection of an omnibus null from a one-way ANOVA.) Olive Jean Dunn came up with what we today call the "Bonferroni" adjustment for multiple comparisons in her 1961 paper.

*Dunn's 'Bonferroni' method can be used in a very broad array of multiple tests scenarios, including ones using paired tests.

*Dunn's test is not appropriate for paired data


References
Dunn, O. J. (1964). Multiple Comparisons Using Rank Sums. Technometrics, 6(3), 241–252.
Dunn, O. J. (1961). Multiple Comparisons Among Means. Journal of the American Statistical Association, 56(293), 52–64.
