This question seems a little complicated, so I will share my vision of payment methods and the life cycle of the order.
Vision of Alan Storm
First of all, I invite you to familiarize yourself with these topics with one of Magento's most famous bloggers, Alan Storm.
This is how I think it works:
Case 1: order with online payment (Paypal, credit card, etc.), payment accepted
Customer Confirmed Order β Magento Created Order β pending_payment Status
An order paid online by the Customer β payment confirmed by the Payment service β payment OK β invoice created by Magento β status pending_payment (not sure about this).
Order shipped by seller β shippig coupon created by Magento β status completed
Case 2: an order with online payment (Paypal, credit card, etc.), payment was refused
Customer Confirmed Order β Magento Created Order β pending_payment Status
Order paid online by the Client β payment refused by the Payment Service β Order canceled Magento β status canceled
Case 3: an order with an offline payment (check / money order, coupon for sale, etc.). Seller invoices before shipping
Order confirmed by the Customer β Order created by Magento β Status pending confirmation Order paid offline by the Customer β payment received by Merchant β order issued by Merchant β invoice created by Magento β status processing
Order shipped by Merchant β coupon created by Magento β status completed
Case 4: an order with an offline payment (check / money order, coupon for sale, etc.). Merchant ships before billing
An order confirmed by the Customer β An order created by Magento β Status pending confirmation An order paid by an offline client β an order sent by the seller β a delivery coupon created by Magento β status processing
Order placed by Merchant β invoice created by Magento β status processing
Hope this topic helps someone in the future.
Let me know if you need more information.