Prior to post Vietnam era; snipers were strictly military personnel; law enforcement used "marksmen", but the military used snipers. Prior to WWI, US snipers were called "marksmen" or "sharpshooters." From WWI onward, nearly everyone used the term "sniper."
With that definition settled; the standard US military sniper rifle from the Vietnam War back...was a standard issue US Rifle; with the exception of the USMC who used bolt action hunting rifles.
With that definition in mind; from the Vietnam War back, US military rifles/USMC hunting rifles were simply top grade, using top grade ammunition (properly weighed grains, fine shaped bullets, etc) and normally "Match" grade ammo, at least in the US Army. The biggest and traditional difference between the standard infantryman and the sniper (in his rifle) was the SCOPE. That made all the difference, and long distance identification.
Post Vietnam War snipers are now commercially/professionally trained at schools, have paperwork identifying them with those special skills (skill identifier codes), they now wear special patches on their uniforms, and have special rifles, scopes, tripods, bipods, uniforms (gilly suits), etc.
Today's "special sniper rifles" have hi-tech "bells and whistles", such as telescoping stocks, special laser range finding instruments and scopes, and barrels with fast rifling twists. They might have stainless steel barrels with cut rifling, the most expensive type of barrel/rifling. And of course the big .50 rifle.
Unfortunately, the scoped rifle may still indicate a sniper...when observed thru binoculars at a distance; but ANY good sniper can do the job with ANY standard issue US Service Rifle...scope or no scope (all Vietnam War snipers HAD TO QUALIFY with iron sights only (M14 rifle, aka XM21, then their scopes). Scopes and super dooper rifles make for fine shooting, but it's the "hunter" behind the gun that's the real sniper.