Simply, amount of damage.
A cut kills very few cells (with the mechanism being mechanical injury). It takes time for that amount of damage to be registered.
When you say “burns felt immediately” it depends exactly how you intend it. As someone has already pointed out, there are reflexes that happen very quickly since it doesn’t require input from the brain. Beyond that, burns damage more cells to be damaged and the damage is more significant. More damaged cells = more pain chemicals released = registers faster.
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