1. The Villain
In the Psych/Ind standard there is a single villain, a figure who is a literal bad apple, and their motivations are evil. Even if these motivations have a sympathetic undertone, they are still irredeemable and monstrous in their caricature. Most of our fantasy villains and Saturday morning cartoon villains are this trope. These villains are also lynch pins in their organizations, and when they are defeated by the hero, everything else crumbles. The best example of this type of villain is Sauron. When the ring is unmade, Barad-Dur, Sauron's great keep collapses on itself and then explodes. The armies of Mordor stop and fall over dead in their tracks.
In the Soc/Int setting, there are key figures, but the motivating force is the organization, the society. Stories about war are functionally Soc/Int because the death of leaders on either side become transfers of power and succession. This muddies out the waters and the enemy leaders are seldom the villains they are made out to be, and the heroic leaders are human and not paragons of light. The Soc/int mode of storytelling allows for a greater range of character motivation.
2. The Hero
As with the Villain, most of the rules are the same in the Psych/Ind vs Soc/Int relationship. The biggest difference between heroes of Psych/Ind and Soc/Int is that in the first narrative the heroes have plot armor, they must have it. If the heroes are slain, there are narratively none to take their place because the structure of the story typically makes the heroes the last line, the only hope, and the Failure is Not an Option play. If Luke Skywalker doesn't confront Vader, Vader never has the Heel/Face turn and that is the only way that the dark lord of the Sith can be defeated.
In the Soc/Int narrative, the heroes are just part of a greater whole, and if they fall, then they fall. There are others who will take up their swords and banners. This comes into conflict with the standard Psych/Ind narrative because we have become institutionalized to the heroes winning, the bad guys losing, the guy getting the girl, snipping the bomb wire with 1 second left, and the otherwise happy ending, with the rare bittersweet self-sacrifice play.
3. The Dues ex Machina Play
A common core of the Psych/Ind story is what amounts to a dues ex machina play. The heroes seldom win in a stand up toe to toe fight. For the victory of the individualist hero to have meaning, the villain's power must be greater, making the hero the underdog. Thus, playing on psychological and individual merit themes, the heroes will pursue a secret plan to exploit an unknown weakness of the enemy and defeat them.
In the Soc/Int narrative, the heroes are just members of a greater force, and when battles are joined, they are just part of it. They can certainly be the most important part of it, but they are not alone. Armies advance, with or without the heroes. The personal beliefs and psychological values of the hero are of little consequence in the greater flow of events, and this likewise applies to those who are on the enemy side.
4. Man vs Society, Society vs Man
Perhaps the most clear cut point, Man versus society is one of the fundamental conflicts in literature and storytelling. In the Psych/Ind conflict if man fights society he is fighting his own society, often by becoming an outcast from it and then overturning it. Rambo is a perfect example, as he is a long man fighting against the authorities of the country he once fought for.
In the Soc/Int story, the struggle of man versus society is that the values and expectations of the society are forced on the people within them. They don't advance the story because they have a personal vendetta against the enemy, but because their 'tribe' is in conflict with the other 'tribe'.
5. Organizations as a Narrative Force
In the Psych/Ind story, organizations tend to be part of the setting, fixed objects or scenery. The characters move through the organizations, changing them, destroying them, or these agencies work as their support system. This fully supports the individualistic narrative, and the exceptionalism of the individual that it encapsulates. Steve Rogers is a good example of this in action. Rogers moves changes organizations with regularity, civilian, US Army, Super-soldier serum, SHIELD, then Avengers. These organizations all have demonstrated flaws, faults, and Rogers is a man above it all.
In the Soc/Int story, more true to real life, large organizations go through people like meatgrinders. They shape the people within them, far more than they are themselves shaped by their members. The thrust of the story is carried by the movement of these greater forces, and Game of Thrones is probably the flagship example of this. While it is easy to assume the story revolves around any set characters, the bloodshed has demonstrated that no one is safe and ultimately the conflicts are between the houses, and the leaders of those houses are the ones burdened with that purpose. It doesn't matter how many heroes and villains are slain, unless the House is extinguished it can stay in the fray.
6. Technology, Magic, and Society
In modern context the great irresistible force is the growth of technology and how it is spreading faster than we can understand. In cyberpunk and sci-fi, the movement of technologies, and technological factions can drive stories in semi-soc/int narratives, but still largely dominated by the psych/ind theme. Magic supplies a similar function, but it is dominated by the individual. The conflicts of fantasy are likewise dominated by the individual, the individual isn't a part of an organization, but is its great representative. The last barbarian, the evil wizard, the lone bounty hunter, the sole knight.
The overall story of King Arthur is the quest for the Holy Grail, which sees a large number of Grail Knights seeking it, and all but one failing, but the search continues regardless of their defeats, deaths, and other setbacks. The enemies of the Grail Knights aren't seeking the Grail for themselves, most are either ignorant of the Grail or don't care about it. They are members of their own agencies, and have their own agendas that have simply come into conflict with the Knights.
Psych/Ind storytelling goes hand in hand with all the tropes of combat choreography, casual coincidence, and plot armor. The individual hero and individual villain HAVE to fight each other, and that means all the artillery, giant robots, meteor summoning spells, dragon attacks, and other weapons in the world are going to stop them from having their climactic dialog and final fistfight. The longer a franchise goes, the larger and more apparent this becomes.
The Soc/Int story doesn't rely on these tropes because the ultimate outcome isn't the triumph of a lone hero, it is the culmination of the conflict. Saving Private Ryan in a psych/Ind story set inside a Soc/Int narrative. The entire US army is advanced from the Normandy Invasion, rife with death, and the characters of the story are just members of that entity looking for a lone individual. Many of the men are killed, but the unremarkable individual is rescued, as they complete their mission as a part of the whole.
Summary - This was inspired by an article breaking down how GRRM has written the Game of Thrones novels as social/institutional storytelling narratives, and while there were characters, heroes and villains, to follow, the main axis of the story was about the coming of the long winter and the different houses vying for the Iron Throne. This exists in stark contrast to most genre fiction which is generally clear cut good versus evil, black and white, order versus chaos, noble heroes versus depraved villains.
Additional Ideas (1)
Another example of this dichotomy is in the classic series Robotech. While it is cobbled together from three different anime, the series was presented as a single story with multiple arcs, and there are different characters who all have their own arcs, their own directions, and they do not serve any single story master. Likewise, there are deaths, and a lot of significant destruction. Many are still sad over the death of Roy Fokker. But the story continues, the Robotech Masters are still fighting for protoculture, and the generations of humans on Earth are still defending it.