I always thought the Saratoga in STIV and Sisko's were the same ship. Why would they be cranking out new Miranda's in the 24th century?
No real dispute here. But newbuilds would explain why a supposedly hard-working fighting ship (rather than a sedately moving science vessel) hasn't worn down from use in the intervening century, even though age and fatigue supposedly claimed two comparable ships from under Jim Kirk.
The damage was already done with the introduction of the "modern" USS Brattain
in TNG, basically. Or to some degree with the reuse of the Excelsior
model in the pilot episode, establishing the continuing use of actual, original Kirk-era fighting ships in Picard's days (which at that point might have been intended to be half a century later still, as per Data's "class of '78" remark). Or, in other words, the lamentable tradition of recycling models from the older movies when making the 24th century TV show. "Emissary" was just keeping up the practice by painting new registry numbers on Sisko's ship - but admittedly could have used the ship with the ST4 registry number just as well.
(...A number in some dispute even today, incidentally. Official sources have quoted something like three incorrect numbers for that ship already, instead of the supposedly visually verified NCC-1887.)
As for the one from DS9 that was mentioned in You are Cordially Invited, I assumed it was Nebula class too being one of the DS9 clips that episode showed a Nebula docked at the station and members of it's crew were at Dax's party.
The party ship was said in dialogue to be the Sutherland
In the teaser to "Wrongs Darker than Death or Night", Worf and Dax seem to be saying that the (unseen) Saratoga
that was to dock with the station would be another harbinger of wild parties. It seems that the writers got their notes about the designated "party ship" confused... This ship is necessarily a "third" Starfleet Saratoga
, as neither of the Miranda
class vessels can be assumed to have survived.
The TNG episode "Aquiel" supposedly involves this "third" ship as well. She is not mentioned in dialogue, so the reference apparently merely comes from one of non-narrated diary entries of the titular character. This may not count as "for real", for various reasons.