Differences between contains and indexOf, Java

I am doing the following programming exercise: The old switcheroo. The statement is:

Write a function

Kata.Vowel2Index("this is my string") == "th3s 6s my str15ng"

Kata.Vowel2Index("Codewars is the best site in the world") == "C2d4w6rs 10s th15 b18st s23t25 27n th32 w35rld"

Your function should be case insensitive to the vowels.

I have doubts when the input is an empty string, I mean when we test with:

import org.junit.Test;
import static org.junit.Assert.assertEquals;

public class KataTest {
  @Test public void test4() {
    assertEquals("", Kata.vowel2Index(""));
  }

}

My question is, why if we use contains, we have to check if input string is empty?

import java.util.*;
public class Kata {
  static final String VOWELS = "AEIOUaeiou";
  public static String vowel2Index/*🔡➡️👆*/(String s) {
    if(s==null || s.equals("")) return "";
    String[] letters = s.split("");

    for(int i = 0; i < letters.length; i++){
      if(VOWELS.contains(letters[i])){
        letters[i] = String.valueOf(i+1);
      }
    }
    return String.join("",letters);
  }
}

Or check if the current string inside the loop is empty:

import java.util.*;
public class Kata {
  static final String VOWELS = "AEIOUaeiou";
  public static String vowel2Index/*🔡➡️👆*/(String s) {
    String[] letters = s.split("");

    for(int i = 0; i < letters.length; i++){
      if(letters[i] != "" && VOWELS.contains(letters[i])){
        letters[i] = String.valueOf(i+1);
      }
    }
    return String.join("",letters);
  }
}

But we can omit the previous condition when we use indexOf:

import java.util.*;
public class Kata {
  static final String VOWELS = "AEIOUaeiou";
  public static String vowel2Index/*🔡➡️👆*/(String s) {
    String[] letters = s.split("");

    for(int i = 0; i < letters.length; i++){
      if(VOWELS.indexOf(letters[i]) > 0){
        letters[i] = String.valueOf(i+1);
      }
    }
    return String.join("",letters);
  }
}

I have also read:

• How to check if a String contains another String in a case insensitive manner in Java?
• Java indexOf method for multiple matches in String

What are the differences between contains and indexOf?‽?