Difference between Absolute and Relative differences

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I was reading a USACO Guide Page on data types and I came across two formulas for the absolute and relative difference in the desired answer and the actual answer that is outputted. This is meant to be calculate the absolute and relative errors but what really is the difference between them? I tried to read this question but could not understand it. From a mathematical standpoint what is this exactly and what are its true applications in programming? Where would I need each type?

Here is an image of the text I was reading:

Image of text from USACO