Depends on the metric defined on the space.
The "normal" Euclidean metric for the distance between two points is the length of the shortest distance between them - ie the length of the straight line joining them. If the coordinates of the two points (in 2-dimensions) are (a,b) and (c,d) then the distance between them is sqrt([(a - c)2 + (b - d)2]
This can be generalised to 3 (or more) dimensions.
However, there are other metrics. One such is the "Manhattan metric" or the "Taxicab Geometry" which was developed by Minkowski. For more information on that, see
http://en.wikipedia.org/wiki/Manhattan_metric
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The shortest distance between any two points is called displacement.
The length of a straight line between those two points.
Distance is the path between two points.
The Length of a path between two points is known as distance.
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