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She pulled out a gun and aimed/pointed it at him.

If she is standing two feet away from him, does it make one of 'aimed' and 'pointed' more appropriate to use than the other?

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pointed is more natural.

Comments  

"Aimed" means she looked through the sights at him. "Pointed" means she merely presented the muzzle to him.

 Clive's reply was promoted to an answer.