According to my knowledge. T-test and Mann-Whitney (Wilcoxon) test the differences between MEANS (not medians) IF data are normally distributed then it means mean almost same as median. So t-test would give us a p-value for difference between means (which equal medians) If data are not normally distributed then I would use Mann-Whitney and report differences between means (with p-value). You can report medians too but there is NO real test to test that difference between medians. That what I know. Any one who tells you use Mann Whitney or Wilcoxon, is not totally accurate because that test is based on assumptions and p-values generated from that test would be more interpreted towards the mean difference (not medians). But I have seen people use that test to for difference between medians in some articles. Again, you would report medians and means and p-value for the means!
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