Question

Both are working, but I am asking if there is any difference or can I just use redirect(); ?

So from these 3 variants, which one is the one that I should stick to?

redirect('/');

or

redirect('');

or

redirect();

Answer 1

If you look at the source you can see that it appends the given URL to the site_url.

function redirect($uri = '', $method = 'location', $http_response_code = 302)
{
    if ( ! preg_match('#^https?://#i', $uri))
    {
        $uri = site_url($uri);
    }

    switch($method)
    {
        case 'refresh'  : header("Refresh:0;url=".$uri);
            break;
        default         : header("Location: ".$uri, TRUE, $http_response_code);
            break;
    }
    exit;
}

So like you said, all those options work.
But I would personally recommend to use:

redirect('/');

If you work with multiple developers this is easier to understand for those who are not familiar with CodeIgniter, since most developer know that “/” refers to the “root directory”.