As far as the test goes, if D is small and p is high, you cannot reject the hypothesis that the two datasets came from the same distribution. The p-value is roughly how often, randomly you would get similar looking data assuming the null hypothesis (in this case that they are drawn from the same dataset)
In light of this evidence, if they are not lying to us, and really each of these sets came from and A-like or B-like distribution, I'd say fairly confidently that:
