It is defined as a line segment
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A best-fit line is the straight line which most accurately represents a set of data/points. It is defined as the line that is the smallest average distance from the data/points. Refer to the related links for an illustration of a best fit line.
If it has defined end points then it is a line segment.
In terms of Euclidian geometry, no lines have end points. A line segment has end points, as it is a section of a defined line of points.
It is simply called the distance between the two points - simple as that. How that distance is measured will depend on the nature of the surface on which the two points are located as well as on the metric for measuring distance that is defined on that space.The common metric in Euclidean space is the Pythagorean distance while on the surface of a sphere (like the Earth, for example), distances are measured along the great arc.
No, because the second line is not defined.