I know that the tilde is used for asymptotic equivalence and symmetry in geometric figures. But here in my highschool textbook it is been used as follows: 
$d = r_1 \sim r_2$
i.e. $d = \left\{ \begin{aligned} r_1 - r_2, r_1 \ge r_2\\ r_2 - r_1, r_2 \ge r_1\\ \end{aligned} \right.$
Now the question is that: Is it acceptable of writers to use such a non-general way of saying this? How can they use such notation in such a vague manner?
According to me it is mathematically equivalent to just saying $d = |r_1 - r_2|$? Am I correct?