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Consider you have two lines are very close to each other, but they are not as if one line is 100 percent exactly on the other line. In other words, suppose that we have picture and if zoom in and zoom out on the graph, we would have something like below:

enter image description here

Now my question is which phrase should be used to describe this two lines the best if we are in the zoom-out perspective as well as when we are in the two-times-zoomed-in perspective. I've only come up with

  1. the overlapping two lines
  2. the coinciding two lines

However, in reality we know they are not 100 percent overlapping. They just happen to be two parallel lines that are very close to each other.

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They are two parallel line segments that are not overlapping at all. This is assuming line segments that are straight and have no thickness. If they weren't parallel and crossed each other, they would overlap and coincide at exactly one point.

Going more directly for the meanings of the two words "overlap" and "coincide", without geometric niceties, two things that overlap coincide for part, but not all, of their extent in a particular dimension. For example, physical objects can't quite coincide, but if one lies on top of another, and doesn't cover it completely, it can be said to overlap it.

For the particular situation you describe above, when the line segments are visible, they don't coincide. When the separation is not visible, they could be said to coincide. But the description would depend on context and what you are trying to say.

An example of overlapping could be represented by these line segments (seen from the top).

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A practical example of overlapping things are roof shingles or tiles. The waterproofing depends on the shingles partially coinciding (in some dimension), and thus forming an overlap.

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