When you implement your own payment method, you can set the order action to authorize, or authorize and capture (sale). I’m quite clear on how they fit into the order management scheme of things. I.e. when you choose authorize, creating an invoice will capture the funds. When you choose sale, the invoice will be created automatically, and an admin will only have to create a shipment to make the order complete.
However, I just found out that there’s a third payment action, called “order” (in \Magento\Sales\Model\Order\Payment::processAction). What does it do?