The details for Prime explicitly refer to it as Two Day Delivery, not shipping.

Prime Membership Benefits

Delivery benefits

FREE Two-Day Delivery: Millions of items delivered fast and free.

FREE One-Day Delivery: Available on more than 15 million items with no minimum purchase.

FREE Same-Day Delivery: Available, in select areas, on over 3 million items for qualifying orders that meet the minimum threshold of eligible items, in as fast as five hours.