Argmin
= Argmin
{title2=$\operatorname*{arg\,min}_{x\in S}f(x)$}
The set of minimizers of an objective:
$$
\operatorname*{arg\,min}_{x\in S}f(x)=\{x\in S:f(x)\le f(y)\text{ for every }y\in S\}.
$$
It is a set of inputs, whereas the <minimum> is an objective value. The <argmin> can be empty if an <infimum> is not attained, a singleton, or a larger set.