MAGeCK uses a parametric statistical test which means that it makes assumptions about the distribution of the data (to be technical: MAGECK models guide RNA counts using a negative binomial distribution). Another example of a parametric test is the Student's t-test.
Mann-Whitney U test is a non-parametric test. This means it doesn't make assumptions about the distribution of the data. In the case of Mann-Whitney U tests, it basically gets you p-values by rank ordering (see https://en.wikipedia.org/wiki/Mann%E2%80%93Whitney_U_test#Illustration_of_calculation_methods ). Consider the following. Situation A: Your treated group has values 7,8,9 and your control group has values 1,2,3. Situation B: Your treated group has values 7000, 8000, 9000 and your control group has values 1,2,3. In both situation A and situation B, the p-value is the same when you run a Mann Whitney U-test. Why? Because the rank ordering is the same! Nonparametric tests are generally considered to be less powerful than parametric tests (look up "statistical power" if you're not sure what that means).