Notice my screenshot above where they call it "First". Also see below where there is no "business" level for on-board experiences. I don't disagree that they go a bit beyond for these flights, but the reality it is still a far cry from D1 and it is not significant enough for DL to denote it as a truly different experience level. Also note that flights to the Caribbean also use J/C/D/I/Z fare codes for First, as do the JFK-SEA/PDX/SAN/DEN/PHX/LAS flights, and yet none of these include lounge access.
http://www.delta.com/content/www/en_...rst-class.html
There is clearly some old/stale code around on the website that calls anything with a J/C/D/I/Z fare class "Business" regardless of the route. The "Business" class designation should only be used on partner flights. For DL equipment, it should either be "First" or "Delta One". There is also the error where the fare search engine will show anything with J/C/D/I/Z fare class as upgrade ineligible even if it is an upgrade eligible route. Again, someone took a shortcut there by solely looking at the fare class and not the actual route and they have yet to fix the bug.
You only see "First" for a J/C/D/I/Z ticket during the booking process. Once it is booked, all you see is "Business" (seat map, reservation, boarding pass, etc). It's been showing "First" during the booking process since a year or so, I was under the impression they were changing the product name to "First" but nothing really happened.
Just checked in for my flight tomorrow in Z and it shows "Business". Even on the GIDS, for these short international flights "Business" is shown for the upgrade list, available seats, etc.