Before I go further in my Sam analysis and theories it's important that I take some time to talk about the freudian aspect gamma mutations and how they work. Don't worry, I'll keep it very simple haha
Short disclaimer: this theory only applies to comics, the MCU and other medias all have their own rules.
The biggest problem with gamma mutations is how a lot of writers ignore how it works and will usually just create yet another Hulk-like, making it a bit inconsistant and so hard to properly understand for readers.
So first let's talk about a few gamma mutants and the power they developped for a better understanding.
Bruce Banner:
We're going to start with the most obvious, Bruce Banner himself. First thing you need to know is Bruce has a DID, so all of his Hulk are actually his alters' Hulk.
Bruce cannot control his mutation because of that. Some are triggered by his stress. People often think it's about anger but really it's about any kind of strong stress (positive such as excitation or negative such as fear, anger, sadness). Some, like Joe Fixit, the Gray Hulk, are triggered by the night (very werewolf coded yes, that's how Bruce's mutation used to work at first actually, transforming every nights). Devil is triggered by death and night, everytime Bruce dies he comeback from the dead at night through Devil Hulk.
No matter the alter though, Hulk is a giant beast, born of Bruce's desire to become strong enough to protect himself and his loved ones but also born of his ressent. Bruce always saw himself as a Monster because of what his father kept telling him and the gamma gave him and his alters a monster look. He was always destructive, he always had anger issues and most importantly his alters were always here.
So the first thing you should note here is rather than giving you what you wish for, the gamma reveal your true self.
Samuel Sterns:
Sam is similar to Bruce in his mutation. Born of the same kind of accident, almost at the same time, from the same experiments, with a painfully hard time to control transformation and most likely (though it's not canon) a DID too.
Unlike Bruce, he can trigger his mutation himself but like him it's very painful and seems kinda difficult, he cannot truly revert back whenever he wants 'cause everytime he does his "other self" fronts while suffering amnesia and Sam (as the Leader) is kinda limited in what he does so he has to guide his other self through dissocation and tricks. He also suffers body dysphoria as a human, so he doesn't revert back, it's very rare and happened only for nefarious purpose or because he was de-powered.
What people fail to understand is Sam's mutation isn't born of a desire to be smart but a desire to be loved. To be like his toxic brother who he admired and saw as the smartest person on Earth 'cause he was very loved while Sam was always being told "if only you were more like your brother" so of course to him being love = being smart, it's about knowledge it's about love. But just like Bruce was always angry and destructive, Sam was always smart and bittert. The gamma mutation gave life to his other alter and his repressed hatred toward a world that casted him away and abused him, but while it enhance the intelligence, it was always here.
It's kinda sad and ironic how Sam always thought he was dumb because of the abuses he went through as a kid and how lots of writers and fans tend to reproduce this abuse by calling him dumb and useless without his gamma power.
The most angry Bruce is, the stronger but the less control he has. Same goes for Sam, the more hate he feels, the stronger he'll be (though for him by strong understand his intelligence and mind power are stronger, not big muscles) but he'll lose control. Have you ever wonder why Sam started as a non-lethal villain, always sparing people and slowly become colder, more heartless and deadly as he started hating more and more through Hulk? If anything him collapsing on the ground and crying, begging Hulk to let him die alone after Hulk freed him from the gamma influence in Immortal Hulk 20 is a proof of him not wanting to hurt and having totally lost control.
Everything about Sam is illusion, he's manipulative and it works for him as well, the illusion of being under control when really it's the gamma controling him. A Sam in control would be Sam in the mobile game Avengers Academy or the first part of his Thunderbolts era as Red Leader before his memory is back.
The second thing you need to note is how gamma mutations are highly related to repressed emotions, thus the reason it's usually fueled by negative emotions. That's the whole message behind Hulk stories, how repressing negative emotions is bad and how they're meant to protect you just like Hulk protects Bruce while being "anger" and the Leader protects Sam while being "hatred" and how they go rampage when the host reject them instead of embracing them like the next people we'll see.
So Bruce is anger and Sam is hatred, what about the others?
Jennifer Walters:
The She-Hulk is about fear. The more she fears, the more powerful, the less control, you get it. And Mariko Tamaki did a wonderful job to show that.
She-Hulk is born of a desire for Jen to be more confident, which she is, that's why she's more in control than anyone else. That also why she's not as muscular as Hulk even with his blood but rather is taller with nice long curly hair. Of course the real reason is sexism and the need to make her "hot" because yes a female character can both be feminist and still rotten by sexism and Byrne's obvious kinky writing for her is a good exemple of that. But through time writers gave it a more "lore accurate" reason. That's why both She-Hulk make sense, the pin-up one and the muscular one.
But confidence isn't the only important part of her mutation, she's also driven by a sense of Justice. As She-Hulk she wanted to punish the bad people who would escape the law through machinations, the people she couldn't beat during a trial.
She was craving power, like Bruce to protect his loved one after his mother's death, like Sam to protect himself.
Betty Ross:
Betty started as Harpy and not as Red She-Hulk, that's why she became Red Harpy recently, way more interesting form to me 'cause not only was she more than a porn fantasy version of She-Hulk but she has a unique very cool look and abilities.
Betty's mutation is born of a desire for independance. She was always someone's tool, through her life but also through her writing. Either to develop Bruce or Hulk or Ross or Talbot, she was always written as a mean to develop a dude rather than her own character. And once she became Red She-Hulk, she quickly became a way to have writers write about their own fantasy rather than her. She's always in the shadow of a man?
Her mutation is kinda meta for that, 'cause she became independant as a woman but also as a character.
She's, like She-Hulk, in total control of her mutation and can revert back at will with no pain in a second.
Now you also notice something all mutants have in common: they all felt powerless at some point and were willing to sacrifice anything to get the power to stand against something they saw as "unfair".
Jackie McGee:
There's a lot of other gamma irradiated we could explore to back this analysis, the whole riot squad made of powerless pitiful people who were enduring their life until they all became gamma mutant with their own specific powers, Abomination who became the monster he was inside, Ross who became Red Hulk, typical "you become what you fear", Samson who became a fuckboy, Amadeus, Skaar, A-Bomb, Tamuz, Lyra, Del Frye etc etc, there's A LOT of gamma mutated, I assume we're getting a new one very soon through Charlie as well. And when they're properly written they're all unique and have their own appearances, abilities and reasons. But I'll end up with Jackie instead.
A lot of people said "Jackie took her power from Hulk and she can see ghosts, like him". But that's the thing, Hulk sees ghosts, Jackie sees the truth, it's a completly different ability.
She's a journalist so she was always digging the truth, make sense to have this kind of power.
But her power is the core of every Gamma irradiation, seeing the truth, that's what it is about, that's why when Sam and Bruce's ancestors are holding a gamma stone and it projects a green light, it's the Leader and the Hulk shadow you see. That's why when Jackie look at Savage Hulk with her gamma eyes, she sees a child crying. Gamma is about revealing who you are, pushing your full potential, revealing your true self, enhancing your biggest qualities as well as givin life to your darkest desires. That's why Hulk is about both the monster and the man. You're given both and it's up to you to choose your path and stay in control, or givin to the shadow.
Sam says it was about forcing the ID to surface, now if you're familiar with Sigmund Freud you might know this specific term but basically the "unconscious mind" Sam is refering to is the Shadow. According to Freud you have three "you" and before Bruce's DID was called a DID, it was a physical metaphore for that, Bruce, Savage Hulk and Joe Fixit where supposed to be the id, the ego and the superego and Prof Hulk was a combination of all that. Now I'm not gonna dive longer in this psychic apparatus 'cause it's complicated enough as it is, I'm here to give you the key to look deeper if you feel like it, because I don't know everything anyway and it would be very egocentrical and clumsy of me to pretend to be what I'm not (a doctor, a philosphe, a psychanalist etc...) and also because I think, on a personal note, that it's healthier and more objective to push people to do their own research.
And then, if you're interested in what I mention, it's up to you to do your own researches. So if you want to know more about the ID, I suggest you to look at Freud and Carl Jung's work on that matter.
But keep in mind that after Peter David's base for the lore, gamma is mutation is 100% inspired by this and your gamma mutation is basically a freudian shadow (which isn't necessarly negative, as we saw through She-Hulk, but could be, like Sam).
This moment in Immortal Hulk is kinda ambiguous, as I said in another post it's not as simple as just "you see Sam and Hulk's shadow so people know who they're talking about" 'cause they also have their face (notice how Robert's face is similar to Hulk's while Samuel is, well, obviously Sam), talking about immortality. Their destiny live on through Sam and Hulk, making them as immortal as their great grandchildren.
But it's not wrong either to talk about a "wish" 'cause that's what all gamma irradiated have in common, they were desperate and powerless. That's why they didn't die of the irradiation like everyone else, because their rage is what seems to be needed to mutate. A wish for power.
A wish yeah, maybe that's why Sam was playing the Devil and making deal with people with wishes when he became the One Below All's (which is kind of the Gamma God) right hand (and then Mask), dangerous wishes with very heavy consequences.
Gamma seems to be following this rule as they all had to sacrifice a part of their humanity for power, maybe that's why the less in control you are (so less human) the more powerful your mutation is, because you need to sacrifice something to get your wish and when you think of it, it's always what their seeking they need to sacrifice for more power. Bruce's peace, Sam's love, Jen's confidence etc...
That's why representing The One Below All (we'll use TOBA now) and the Place Below as a metaphor for Hell and Satan makes more sense than just "booouuuuhh all evil bad guys", because dealing with Gamma is dealing with the Devil's power, it's the same kind of twisted deal Gamma has to offer, a poisonned gift and a curse. A trap rather than a gift. That's how the Devil works too, making deal with you.
In conclusion
I think the very best way to understand how gamma mutations works and how it's about miserable people wanting a better life is to read Hulk Ground Zero (Incredible Hulk 345), Peter David is the first one who added depth to the gamma lore and who tried to define it, to explain why some people survive the exposure and other don't and I think he did a great job with that issue. If you need to read one issue to understand it is this one as it focus on the casual life of people who will become gamma spawns.
And that's what they were, they didn't like their life, they were suffering it rather than living it, but they were trying to freed themself from it, that's what the gamma is about, will. As miserable as you think you are, the will to survive and the will to live, the will to get what you think you deserve.
Most people will say "it gives you what you wanted" but that's the tragic irony, what you need to be is often what you already are and Hulk is a tragedy rather than a super hero story, so are gamma mutations.
Enjoy~