If $x$ and $y$ are distinct, then that means they can be distinguished, or identified as being different from each other.
- $x$ is distinguished from the other elements of $S$
- $x$ is endowed with a property that the other elements of $S$ are specifically deemed not to possess.
Such an element is identified as being distinct from the others.
Two objects are indistinguishable if they can not (in a particular context) be told apart from each other.
So, two objects may be distinct but (at a given level) indistinguishable, like identical twins.