This part of the code will be called multiple times unnecessarily

// If both the positions are updated, update the shortest distance
if (position1 != -1 && position2 != -1) {
    shortestDistance = Math.min(shortestDistance, Math.abs(position1 - position2));
}

Scenario:

String[] words = { "a", "c", "d", "b","x" ,"a" };
String word1 = "a";
String word2 = "b";