Finding the Error Between Two Points

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ACLerok
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if given two points each with different x and y coordinates, what is the best way to define the error between these two points?
 
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How do points have an "error"? About the only measurement I see is the distance between the points:
[tex]\sqrt{(x_1-x_2)^2+ (y_1-y_2)^2}[/itex][/tex]
 
Like if one point is the true location and you want to say how much off the second point is. I guess the distance between them would be the best way to display this...
 
say there are two boxes that are not equal in size but close that are overlapping. is there an equation that can calculate how much the "wrong" box is covering the "true" box in percentage form?