The shortest distance between any two points is called displacement.
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The shortest distance between four points is a straight line to and from each individual point. If all four points are aligned, the result will be a single straight line through all four points.
Multiple straight lines.
Distance.
The two points and the centre of the earth define a plane, and the intersection of this plane with the surface of the earth is a circle - the "Great Circle". The shortest distance between the two points is the smaller of the two arcs on this circle.
The shortest distance between two points is a line, or a line segment. If you have two points, and you know they are part of a line, you can connect them with a line.