How is delivery and payment status on order level used?

Delivery status and payment status can be found both in General group and on every payment/delivery. How are these different statuses used i Litium?

Litium do not use Payment and Delivery statuses in order level. They can be customized by the projects.
Litium accelerator uses the Order status (Order level), Delivery status (for each delivery) and Payment statuses (for each payment). Order statuses and delivery statuses can be customized, payment statuses are fixed and cannot be customized.