Yes, those options in the example are the same, but in your actual code will be different, I'm nearly trying to highlight that the only thing that gets changed is the options inside the function, and not the function itself. those options will effect settings like arrow placement and such, not just the style.
so to recap:
create a test page with a small form.
add jQuery validation to it with the settings you wish to use on the checkout form.
copy the CSS link and use it on the checkout page inlace of the other style link
Copy the options inside the opts function, and paste them over the opts in the checkout page.
I can't say why it is not working when you try to edit it on your checkout page, but this should work as a work around.