The ideia of minimality
is built into the meaning of the word distance.
(The distance between two points
is the length of a shortest path between the points.)
Therefore,
the expressions
shortest distance
,
minimal distance
,
and smallest distance
are redundant.
The expression a largest is, almost always, more correct than the largest because in general there is more than one largest element.
What is the difference between the words variant (of a piece of code) and invariant (of an iterative process)?