namespaceを使うようです｡
https://github.com/dapphp/securimage/blob/master/securimage.php#L427
試していませんが､下記でどうでしょう｡

form.html

<form method="post" action="comment_form.php">
 <img src="./securimage_comment.php"><br />
 <strong>Enter Code*:</strong> <input type="text" name="captcha" />
</form>
<form method="post" action="contact_form.php">
 <img src="./securimage_contact.php"><br />
 <strong>Enter Code*:</strong> <input type="text" name="captcha" />
</form>

securimage_comment.php

<?php
require_once 'securimage.php';
$img = new Securimage();
$img->namespace = "comment";
$img->show();

comment_form.php

<?php
require_once 'securimage.php';
$img = new Securimage();
$img->namespace = "comment";
if ($image->check($_POST['captcha']) == true) {
 echo "Correct!";
} else {
 echo "Sorry, wrong code.";
}

contactはcommentをcontactに変えます｡