I've read in the library manual for test ks.test that

The possible values "two.sided", "less" and "greater" of alternative specify the null hypothesis that the true distribution function of x is equal to, not less than or not greater than the hypothesized distribution function (one-sample case) or the distribution function of y (two-sample case), respectively. This is a comparison of cumulative distribution functions, and the test statistic is the maximum difference in value, with the statistic in the "greater" alternative being D^+ = max[F_x(u) - F_y(u)]. Thus in the two-sample case alternative = "greater" includes distributions for which x is stochastically smaller than y (the CDF of x lies above and hence to the left of that for y), in contrast to t.test or wilcox.test.

Unfortunately I failed to understand this difference between (I guess one sided) wilcox.test and ks.test. It seems, that both test for displacement of one distribution versus another. Does anyone can shed some light on it, please?