PHP - How do I partially compare elements in 2 arrays

I have 2 arrays:

$arr1 = array('Test', 'Hello', 'World', 'Foo', 'Bar1', 'Bar'); and
$arr2 = array('hello', 'Else', 'World', 'Tes', 'foo', 'BaR1', 'Bar'); 

I need to compare the 2 arrays and save the position of the matching elements to a 3rd array $arr3 = (3, 0, 2, 4, 5, 6); //expected result, displaying position of matching element of $arr1 in $arr2.

By 'matching' I mean all elements that are identical (ex. World), or partially the same (ex. Test & Tes) and also those elements that are alike but are in different case (ex. Foo & foo, Bar & bar).

I've tried a series of combinations and of various functions without success, using functions like array_intersect(), substr_compare(), array_filter() and more. I'm not asking for the exact solution, just something to get me on the right track because i'm going around in circles all afternoon.

This seemed to work for me, but I'm sure there are some edge cases I'm missing that you'd need to test for:

foreach( $arr1 as $i => $val1) {
    $result = null;
    // Search the second array for an exact match, if found
    if( ($found = array_search( $val1, $arr2, true)) !== false) {
            $result = $found; 
    } else {
        // Otherwise, see if we can find a case-insensitive matching string where  the element from $arr2 is at the 0th location in the one from $arr1
        foreach( $arr2 as $j => $val2) {            
            if( stripos( $val1, $val2) === 0) {
                $result = $j;
                break;
            }
        }
    }
    $arr3[$i] = $result;
}

It produces your desired output array:

Array ( [0] => 3 [1] => 0 [2] => 2 [3] => 4 [4] => 5 [5] => 6 )