Hi,
You can create custom fields of the type user and/or address with the essential edition via the menu Display->Custom fields. Make sure they are published and the front end activated. They will appear on the checkout when not logged in.
For the "Totally customizable checkout process", it refers to the checkout workflow option of the configuration and the other numerous options of the Checkout tab of the config.
Finally, in the Business edition, you will indeed have additional types of custom fields and more particularly the type "order" which is attached directly to the order and displayed on the checkout with the view "fields". That's not mentioned on the feature list but it's on the Business edition page:
Custom fields for orders and entries as well as custom file type