I've seen 1-day and even same-day shipping on a variety of items, so I suspect it's determined by some arcane combination of user location and item logistics.
They used to offer guaranteed two-day shipping and a paid upgrade to one-day shipping; now they just have "Prime Shipping" as the parent said, and what "Prime Shipping" means varies from item to item and time to time. It can mean one-day. I don't think I've ever seen same-day shipping, but I'd imagine I just don't live close enough to a fulfillment center.