As far as the actual link between an Order and a FulfillmentOrder goes, the FulfillmentOrder has an attribute called "order_id". That attribute is a reference to the unique id of an Order object. The easiest way to think about the Order/FulfillmentOrder relationship is as a "parent"/"child" relationship. You can have one or more FulfillmentOrders (children) that are part of an Order (parent).
This illustration is from the Fulfillment object API docs: