In Newtonian three dimensional space, two points can create a line, three to "define" it. In Einsteins "time-space", a minimum of four points are required.
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There is only one line (or line segment) that can be drawn between two distince points.
In classical or Euclidean plane geometry two points defines exactly one line. On a sphere two points can define infinitely many lines only one of which will represent the shortest distance between the points. On other curved surfaces, or in non-Euclidean geometries, the number of lines determined by two points can vary. Even in the Euclidean plane, two points determine infinitely many lines that are not straight!
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