There is a checkbox in the checkout wizard for "Include shipping fields on checkout page"
It should always create the shipping fields as long as that checkbox is checked, the checkout form you have seems to be what would result if that checkbox was not checked.
The url they gave you is for direct pay api, which requires the card details to be passed in.
Looking through their documentation, it appears the original url the eCart used was correct, but you might try:
The url should definitely not be the vspdirect version if you aren't asking for credit card details from your site.