The evolution often moves from a raw, instinctual terror of the unknown into something more complex. At first, it's all about the jump scares—the weird noise in the house, the shadow that shouldn't be there. That's the surface-level dread. As the story unfolds and the threat becomes more defined, the fear morphs. It becomes less about the monster under the bed and more about what the monster represents. It starts to infect their daily life, making them question their sanity or their safety in places that were once secure.
Then you get the real gut-punch: the fear of loss. Not just of their own life, but of the people they love, their sense of self, their morality. A protagonist might start out scared of a ghost, but by the climax, they're terrified they'll have to become a monster themselves to survive. Stephen King's 'It' does this brilliantly—the kids aren't just afraid of Pennywise; they're afraid of forgetting each other, of losing the bond that got them through it. The final stage is often a kind of grim acceptance or a fury-born courage. The fear doesn't vanish; it gets integrated. They're still terrified, but they're moving forward anyway, which is way more interesting than a character who's just perpetually screaming.
You see this arc in a lot of Gothic novels too, where the fear of a supernatural antagonist gradually reveals itself as a fear of a repressed truth or a corrupted lineage. The evolution is the story, really.