how do pawns and characters move

The CharacterMovementComponent moves the object, for Characters. Characters are a kind of Pawn. However, other kinds of Pawns and Actors use different MovementComponent implementations. For example, there’s a ProjectileMovementComponent, for projectiles. The simulation of each of these kinds of movement, is done in the movement component implementations.

Separately, the physical interaction (collision) with the world, is done by the physics system – Chaos, in UE5 – where the character actor moves the collision proxy, and reacts to collision callbacks from that system.

Finally, I feel that it’s OK to say “I read your code and it didn’t answer my question.” However, I don’t think you get to complain more than that, that it doesn’t answer the question – everyone here is trying to help you for free and if they feel that they’re hearing whining in response, they will be less likely to attempt to help next time.
If you see this same result in other questions you ask, perhaps you should look at the common element in all of those questions for some insight?

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