Imagine two lists of two-dimensional coordinates:

    listA = RandomReal[{0,100},{202,2}];
    listB = RandomReal[{0,100},{97,2}];

I'm attempting to quickly generate a new series of lists, `outputListA` and `outputListB` consisting of the set of points in `listA` and `listB`, respectively, that are within some Euclidean distance $D$ of a point in a list for which they are not a member (i.e. points in `listA` that are at most a distance `distCut` from at least one point in `listB` and vice versa).

This isn't the right way to do things (it takes $\approx 88$ milliseconds for sizes of `listA` and `listB` shown), but it hopefully illustrates what I'm trying to do:

    listA = RandomReal[{0, 100}, {202, 2}];
    listB = RandomReal[{0, 100}, {97, 2}];

    outputList = {};
    distCut = 1;

    For[x = 1, x <= Length[listA], x++,
     For[y = 1, y <= Length[listB], y++,
       If[EuclideanDistance[listA[[x]], listB[[y]]] <= distCut,
         outputList = Append[outputList, {listA[[x]], listB[[y]]}];
         ];
       ];
     ];

    outputListA = Intersection[outputList[[All, 1]], outputList[[All, 1]]];
    outputListB = Intersection[outputList[[All, 2]], outputList[[All, 2]]];

    Length[outputListA]
    Length[outputListB]

A smarter way to proceed might be to round values in `listA` and `listB` to a multiple of `distCut`, and then check for values in the rounded lists that are equal.  However, I can't think of a good way to do this that avoids unnecessary attrition / misses points.