In addition to marksmanship and long range shooting, military snipers are trained in a variety of tactical techniques: detection, stalking, and target range estimation methods, camouflage, field craft, infiltration, special reconnaissance and observation, surveillance and target acquisition.
The verb "to snipe" originated in the 1770s among soldiers in British India in reference to shooting snipes, which was considered an extremely challenging game bird for hunters. The agent noun "sniper" appears by the 1820s. The term sniper was first attested in 1824  in the sense of the word "sharpshooter".
A somewhat older term is "sharp shooter", a calque of 18th-century German Scharfschütze, in use in British newspapers as early as 1801.