Amazon Pay Checkout v2 through Amazon's own SDK: placing the order creates a one-time "pay now" session for the order's total with its shipping address, the customer confirms on Amazon's page and comes back; the return completes the session and captures or authorizes the charge. Refunds and invoice captures go through the charge. No Amazon script on the shop's pages.
The Amazon Pay settings in the admin.
What it does
Pay now on Amazon's page, no button script on the site
Authorize and capture, or authorize and capture on invoice