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.