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 largest vs a largest

The expression  a largest  is, almost always, more correct than  the largest  because in general there is more than one largest element.

Variant vs invariant

What is the difference between the words variant (of a piece of code) and invariant (of an iterative process)?