What is the difference between standard deviation and average of absolute difference of any two numbers?

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For a set of data $(x_1, \ldots, x_n)$ and its mean $x'$, the standard deviation is calculated by

$$ \sqrt{\frac{\sum_i(x_i - x')^2}{n}} $$ , while the absolute difference of any two numbers can be computed by

$$ \frac{\sum_i|x_i - x_{i+1}|}{n}. $$

What is the difference of those two values?

(Added Below:) Both measure average distance among data points. How do they differ and how are they used in practice?