PHP expresses two different strings to be the same

"608E-4234" is the float number format, so they will cast into number when they compares.

608E-4234 and 272E-3063 will both be float(0) because they are too small.

For == in php,

If you compare a number with a string or the comparison involves numerical strings, then each string is converted to a number and the comparison performed numerically.

http://php.net/manual/en/language.operators.comparison.php

Attention:

What about the behavior in javascript which also has both == and ===?

The answer is the behavior is different from PHP. In javascript, if you compare two value with same type, == is just same as ===, so type cast won't happen for compare with two same type values.

In javascript:

608E-4234 == 272E-3063 // true
608E-4234 == "272E-3063" // true
"608E-4234" == 272E-3063 // true
"608E-4234" == "272E-3063" // false (Note: this is different form PHP)

So in javascript, when you know the type of the result, you could use == instead of === to save one character.

For example, typeof operator always returns a string, so you could just use

typeof foo == 'string' instead of typeof foo === 'string' with no harm.

You need a Ajax call to pass the JS value into php variable

JS Code will be (your js file)

var jsString="hello";
$.ajax({
    url: "ajax.php",
    type: "post",
    data: jsString
});

And in ajax.php (your php file) code will be

$phpString = $_POST['data'];     // assign hello to phpString 

Ah, finally I got it. It was quite stupid of me.

Comparison involves not only "is equal" but also "less than" and "greater than". And for the latter two it is obviously critical to cast numerical operands before comparison, because numbers often being represented in PHP as strings, and 11 have to be greater than 9 even if both stored in strings.

So, as compare_function() does all the comparisons at once, returns either 1, 0, -1 to tell if first operand is bigger, equal or less than second respectively - well, it's fairly explains, why operands being cast.