Which method is likely to give you features that overlap with the source layer?

The method that is likely to give you features that overlap with the source layer is the one involving features that "are within a distance of" the source layer. This approach identifies features that fall within a specified distance from the boundaries of the source layer, thus allowing for overlapping areas between the two datasets.

When you use this method, you can obtain features that are not just directly touching or intersecting the original layer but also include those that are slightly apart yet still relevant based on the distance parameter set. This is particularly useful in analyses where proximity matters, such as in buffer analysis—where features within a certain radius of a target area are included for assessment.

This spatial relationship can capture a broader set of overlapping features compared to the other methods. For example, using "share a line segment with" might only consider those features along specific lines, which may not capture broader spatial relationships. Similarly, methods that involve touching the boundary or containing features typically look at more constrained relationships that do not inherently emphasize overlap in the same comprehensive way that a distance-based approach does.