Studying if/else vs if/if statement

I was trying to write a code where all the 0s will be moved to the right of the array. I just used a left and a right pointer.

 public class Solution {
      public int[] moveZero(int[] array) {
        // Write your solution here
        if (array.length==0) {
          return array;
        }
        int left=0;
        int right=array.length-1;
        while (left<=right) {
          if (array[left]!=0) {
            left+=1;
          } 
          if (array[right]==0) {
            right-=1;
          } else {
            int temp = array[left];
            array[left] = array[right];
            array[right] = temp;
            left+=1;
            right-=1;
          }
        }
        return array; 
      }
    }

I know here I should use the if/else if instead of if/if, that's why I have the index out of the bound error. But I don't understand why? If I have the if/if statement, what's the difference does that make rather than using if/else if in this question?

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