To the best of my knowledge, the Mann-Whitney U test (also called Wilcoxon-Mann-Whitney) is for comparing only two unpaired groups, while the Kruskal-Wallis test is used for comparing two or more unpaired groups. Comments like this thread and explanations like this Wikipedia page or this website confirm this.
However, JMP does not have a Kruskal-Wallis test. Instead it has a Wilcoxon test, which is basically a Wilcoxon-Mann-Whitney (or a Mann-Whitney U) test because it is used only for comparing unpaired groups (unlike the Wilcoxon paired ranks test which is used for paired data).
Interestingly, this Mann-Whitney U test can be used for comparing more than two groups as well. Please see JMP's catalog for more details on its non-parametric tests and the use of Mann-Whitney U instead of Kruskal-Wallis in JMP. This is the first time I am seeing a statistical program uses the Mann-Whitney U for comparing more than 2 groups, as if it is a Kruskal-Wallis test. It also outputs chi-square values, which is strange for a Mann-Whitney U test comparing two groups, although perhaps useful for a Kruskal-Wallis comparing more than two groups.
Is this procedure used by JMP correct? Are Mann-Whitney U and Kruskal-Wallis tests exactly the same from a mathematical standpoint, allowing Mann-Whitney to be used for three or more groups? If yes, why Kruskal-Wallis even exists as a separate test? If they are not exactly the same, then perhaps JMP's method of comparing three or more groups using a Mann-Whitney U test is not theoretically correct.
I compared the results of Mann-Whitney U and Kruskal-Wallis on a dataset. Their outputs were identical, implying that a Kruskal-Wallis can be used instead of a Mann-Whitney U (at least in some situations). But can a Mann-Whitney as well be used for comparing 3 or more groups (like a Kruskal-Wallis)?