I dont see how this is ‘off topic’ since you started the topic...?
That aside, when i get something same day from amazon it seems to fit two criteria: 1) its stocked by amazon in a local hub or “fulfillment center” and 2) it get delivered via independant courier. In the dc area a company called “laser shipping” seems to have a contract for a lot of it.
It appears that they have independant contractors come by once a day for packages stocked in those hubs and if your address is within “x” miles of said hub they know the delivery can be same day. Things shipped via us mail, fed ex and ups all have to go through their hubs and add a day or more. Here in dc they offer (based on delivery address im sure) free same day on a lot of (usually) smaller items, generally with the caveat that you order st 35$ bucks worth of merchandise. I have taken advantage more often than i care to admit.