Note this is based on a standard Magento installation and doesn't take into account any third party extensions you may have doing things with orders statuses...
In Magento, if you create a shipment from an order, but don't create an invoice for an order, it will become 'processing'.
If you then create an invoice, it will become 'complete'.
If you create an invoice for an order, then you create a shipment for an order that order status will be complete.