Use - Compare two groups. It is a non-parametric ver of the t test.
Note the Mann-Whitney U test is essentially the same as the Wilcoxon rank sum test.
Requirements / Assumptions:
8-10 observations in each group.
Data distribution - no requirement
Variances - Some sources say equal / similar variances are required or state that the data come from a common population.. while others do not discuss it. Some authors recommend if the variances are large to use the Brunner–Munzel test (add references and summary)
Useful resources: