What exactly do they do? How are they different from the Order of Shadow as well? I know the Order of Shadow wants to militarize Ionia. At first I was under the impression that the Navori Brotherhood was the same group, but that is incorrect, it seems. Can anyone help me figure this out?
They are an extremist nationalist group opposed to both Irelia and the Order of Shadows.
Looking at Irelia's bio we can find those quotes:
Across Navori, dissenting voices began to band together. A resistance was forming, one that would not rest until Ionia was free once more. Irelia joined their ranks, performing her cherished dances for them in the woodland camps, to preserve some vestige of their vanishing culture.
She was barely fourteen years old when she found herself back at the Placidium. Her band of resistance fighters joined the militia who had sworn to guard the monasteries and wild, sacred gardens.
...
This victory, the Great Stand at Navori, ensured that everyone in Ionia knew the name of Xan Irelia, and looked to her for leadership. Reluctantly, she led the growing resistance for almost three years of grueling battle before her triumph at Dalu Bay. There, she finally cornered the defeated Admiral Duqal, and exacted the vengeance she had sought for so long.
(Important note here is that the invasion was stated to have ended 7 years ago, when Swain took power of Noxus and retreaded the troops from Darkwill's impossible campaigns. And since the Battle of the Placidium is stated to have ended a decade ago, this means that Irelia stopped to lead this resistance when the war ended)
So, while it was stated that the "Navori Resistance" was formed during the war, it wasnt said that it ended after the war nor that Irelia was the last leader.
So even if it wasnt confirmed, I believe that the Navori Brotherhood was formed when Irelia stopped to lead the resistance a new, unknown leader came in.
That part said, we know few things about the Navori Brotherhood's goals and ideology, most of it comes from some quotes in Irelia's color story:
Irelia held her stance. She looked down at him, this devotee of the Brotherhood, on his knees in the mud. He had been pierced over and over by her blades.
“We could have been strong... United as one people...”
He spat blood on the ground, his eyes burning with hatred. “If you will not lead Navori, the Brotherhood will.”
"The Brotherhood would grip this land in an iron fist. No better than Noxus…”
So from that we can gather that the Navori Brotherhood wants to unite the entire Ionia(beggining with the Navori province) and militarizy the entirity of Ionia, basically turning Ionia into Noxus 2.0 but with more magic.
They also opearte outside of the Navori province and are extremly agreesive to foregneirs, as seen in Ryze's cinematic(if you look at the map it confirms that those warriors were from the Navori brotherhood and that it happened in an island far away from Navori).
I'm not sure if the differences between the Order of Shadows and the Navori brotherhood were ever mentioned, Waaaaaaaaaarghbobo did mention a possible connection in this post: https://boards.na.leagueoflegends.com/en/c/story-art/JjQEuhgJ-zeds-new-lore?comment=0000
Zed forms his own order— related to the Navoi militia group. (Spelling?)
I believe the principal difference would be that Zed's order is the only group in the entire Ionia that agrees with the usage of Shadow magic.
I hope that this helped you to understand what they are ^^
