Demo VS live examples

Hi,
i see that your http://demo.vuestorefront.io/ behave differently from your live examples eg. https://zadig-et-voltaire.com/eu/fr

On your demo whole checkout process is on your frontend, but on live examples checkout is on sparate domain eg. “checkout.domain.com” and it’s magento.

Why you decided to redirect to magento instance in your live projects for checkout?

Do you have custom modules for magento or any sample code that is responsible for restore customer cart/session from token (in url) ?