Let us examine the data. Let us try to infer with greater precision what is the nature of the difference between the first data set where point set 1 and point set 2 are independent and are each uniformly distributed over the unit square and the second data set where one point set seems to be closer to the other. It seems that it is not just that one point pair are closer to each other, but there are a few point pairs which seems to be closer to each other.

Each point from point set 1 has a closest point in point set 2. Each point from point set 2 has a closest point in point set 1. As there are 10 points in each point set, there are 20 such closest point pairs, not all of them necessarily unique. There might be duplicates.

Red denotes points from point set 1. Green denotes points from point set 2. The first plot is a sample showing the pattern when point set 1 is independent of point set 2 and both are uniformly distributed over the unit square. The second plot is a sample showing the pattern when point set 2 is moved closer to point set 1