'Sharpshooter' often refers to military or law enforcement precision shooters. During the battle, the sharpshooter provided cover for the advancing troops.
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Skill Level
Implies extraordinary skill, not just good with a firearm. After weeks of training, she earned the title of a sharpshooter.
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Target Shooting
Also used for non-military precision target shooting competitions. He's not just a hobbyist; he's a competitive sharpshooter.