Basically I don't want the page to redirect to "action.php" this one time.
I need it to stay on the same page. I know about action="" but I still need it to redirect, just not this one time.
Is there a PHP function that makes the redirect to stay on the same page, the same functionality as action=""?
That's nothing you can do with php as php is a server side language and so a redirect (or another call) needs to be made so php is executed. You can do something with JavaScript as it's a client side language.
Something like (note: will likely not work):
<form action="" onsubmit="return false;">
</form>
There are different event handlers where you can call ".preventDefault()" and such things. You need to look which one is the best, I'm not that familiar with JS

I assume you are trying to redirect to the same page regardless of the outcome status (error, success, preview, etc)?
Lets say the following:
if($mybb->get('action') == 'foo')
{
$success = array();
if($mybb->request_method == 'post')
{
$success = 'The form was executed successfully.';
}
$success or $success = '';
echo $success;
echo $form;
}
Now have the form pointing to action=foo, the first time the user visits the page it will be presented with only the $form and $success emptied. Once the user summits the form, $success will be filled with a message.
Sorry if I don't explain myself well but I think this is what you are trying to achieve.