The Sith Eternal is the cult of Sith loyalists that serve Palpatine on Exegol. The Final Order is the fleet the Sith Eternal created to enact Palpatine's final conquest of the galaxy. It's just a fancy name, and could easily be referred to as the Sith Eternal fleet.
Sith Eternal do not pretend what they are. The Final Order takes away the mask that the First Order used to pretend what they are.
I think one of the key things is to remember that the First Order was not an actual Empire despite appearances, it was a military junta. That was a distinction even Abrams made during the promotional period for TFA. They were a fleet that had survived for years in the Unknown Regions and grown in strength. That fleet eventually reestablished its connection to the various governments that formed the Imperial Remnant as a faction in galactic politics, giving rise to the First Order as a publicly known entity. But the Imperial remnant never played a role after TFA, so the First Order remained a military force with no real government to command it. I doubt the former Imperial politicians were annihilated in the Hosnian Cataclysm, but they were clearly only useful prior to that, to give the First Order an appearance of political legitimacy as it continued to grow in strength and expanded into the outer rim of known space. But the Imperial political bloc were revealed as nothing but pawns for the generals and Supreme Leader once the trappings of a galactic government were vaporized. The Final Order and the Sith Eternal, by contrast, are a separate Imperial faction that survived the collapse of the Empire in almost complete isolation. The Sith were the theocratic heart of this faction, and the Final Order was its fleet, far less independent and more mechanized than the First Order had been. These two operate as a united faction, much like the Empire and its fleet did. And that’s partly because they are not a force that was reborn after Imperial collapse, they are a part of the Empire that never collapsed. And the First Order served them unknowingly as both a vanguard force to weaken the galaxy and a public enemy to keep attention away from the secret enemy that was still vulnerable and hiding even deeper in the shadows.
@Sauron_18 The Sith Eternal are essentially HYDRA, they have operatives everywhere and sometimes indirectly control sith. If Snoke is part of the Sith Eternal then the Sith Eternal have a agent in the highest echelons of the First Order. The real question is, when did the Branding change happen and that Fleet official dub itself the FIRST ORDER with the flag and the stormtrooper armor etc etc.
I think the real question is how much of the First Order developed independently from Snoke and Palpatine before they took over.
I personally think the more one thinks about the distinction between the First Order and the Sith Eternal, the more silly it becomes. From where The Mandalorian and The Bad Batch look to be heading, it seems that it was the imperials/the imperial remnants, who were developing the cloning technology to *possibly* clone Palpatine and do some form of midichlorian transfusion (?). Therefore, given that The First Order are imperial remnants, they should have been the ones to resurrect Palpatine. I think the Sith Eternal thing would only really work if it were not Palpatine, but some other Sith master/Lord heading it up.
I don't get it either how the factions that descended from the Empire are supposed to work. There's Palpatine and the Sith Eternal in the shadows puppeteering everything. The Sith Eternal created Snoke, who takes over the First Order for them, and built a fleet of planet-killing Star Destroyers called the Final Order. It seems there are three separate classes of Imperial remnants; the Imperials that the Emperor had deemed worthy that fled into the Unknown Regions, the failures who were absorbed by the New Republic that became the Centrist political party in the Senate, and the warlords that just wanted power for themselves and kept operating. From what we've seen so far the first two classes of Imperial remnant unified together under the banner of the First Order, but I'm wondering if the warlords (the Moff Gideon and the Client types) were assimilated into the FO or wiped out.
To really help answer these questions, it would be great of the TV shows explain more. As I would be thrilled to learn about this faction of remnants Moff Godeon is leading and where they will fit in once the FO is created or if it's already created. And what is their relationship to the Sith Eternal? As it seems clearly they are using Grogu's blood/DNA for Snoke or Palps and thus working for the Sith Eternal. It would be interesting to see other factions not wanting to explore this direction causing a split.
It would have been nice to have even just a little bit of that in the films. two or three sentences of dialogue would've easily covered it... The fact Abrams even addressed this in the lead up to TFA makes this lack of clarification even more frustrating!