Equivalence of set of minimizers of different optimization problems

Question

Let $N = \{1,2,\ldots,n\}$ denote a set of items, $s \in \mathbb N^N$ the size of each item, $x \in \{0, 1\}^N$ a decision variable indicating whether item $i \in N$ is part of a package and $C > 0$ a capacity. I am wondering whether the following relationship holds: \begin{align} \arg\min_{x} |C - s \cdot x| = \arg\min_{x} (C - s \cdot x)^2. \end{align}