The Mann–Whitney U test has the following interpretation reported on wikipedia:

[...] is a nonparametric test of the null hypothesis that, for randomly selected values X and Y from two populations, the probability of X being greater than Y is equal to the probability of Y being greater than X.

I had intuitively taken this to mean "one variable tends to be larger than the other", but I recently encountered different notions of stochastic dominance including statewise dominance, first order dominance, second-order dominance, third-order dominance, and a less-specific notion of higher-order stochastic dominance.

Which form of stochastic dominance is tested for using the Mann–Whitney U hypothesis test?