It’s possible my interpretation is wrong, but as you said, there are plenty of Prime shipments that are delivered in 3-5 days. It happens to my orders all the time. That alone seems to say that it is 2-day shipping, and not 2-day delivery. If you call up and want some sort of credit on that 5-day Prime delivery Amazon will say, “no, because we shipped it in two days, which is what we promised”.
Most of the time Amazon does better than what they promise and gets items to a customer within two days, but as someone else said that just makes buyers think 2-day shipping means 2-day delivery (when it really doesn’t).
The written requirements are just what amazon “writes” as shipment and delivery time on any individual order.