Kruskal Wallis vs. Mann-Whitney-U Test

As far as I understand Kruskal Wallis is a test for more than two groups Mann-Whitney-U-Test is just for 2 groups

Just for fun I used Kruskal Wallis for two groups as well. I noticed that the statistics are different from Mann-Whitney, but the p-values were exactly the same.

Is this correct? If so, why do I need a Mann-Whitney-U-Test at all? I could always do the Kruskal-Wallist-Test for any group size. Or did I make an error?