Finally done the two tests...

 

Both are non-parametric tests, the statistics of which are independent of the distribution from which the samples are obtained. M-W test are used to examine whether 2 samples, when obtained independently, came from the same distribution. K-S test does the same thing, but also examines, when one of the emperical cdf is substituted by a theoretical cdf, whether a sample came from a distribution that is identical to the hypothetical cdf used in calculating the test statistics.

 

R code (stripped)