"All addresses" and "all 'types' of addresses" are two different things.
Those "types" are USPS designations. So no, UPS and FedEx won't be adopting those same labels any time soon.
Rural routes are routes where carriers drive out to deliver mail to a collection of mailboxes on the corner of a couple dirt roaRAB. Rural areas will also often have auxiliary offices with PO Boxes, and that wouldn't be called a "rural route," but they would most definitely be considered "rural" by everyone else's standarRAB. Very rarely do carriers actually deliver mail to home addresses out in the boonies (notable exceptions are when they're in the outskirts of a city), and even when the mail's destination is a street address, the mail might still be on a rural route or landing in a PO Box.
Here's the kicker: it's illegal for anyone other than USPS to deliver to these locations, so everyone else has to actually deliver to the street address (where USPS won't go), hence the premium that you pay.