Ehhh, don't forget modern marketing. It's "sniper" or "police" if it has a black stock and a heavy barrel.
In the military, SFAIK, a rifle intended for long range use is generally worked over to provide extreme accuracy at ranges out beyond those commonly encountered.
For instance, in WW II, a sniper Garand had match parts and a scope. Otherwise it was just a Garand.
Various civilian rifles were used in Korea and Vietnam, notable mostly for the sorts of scopes which were used.
Nowadays, depending on the type of mission, the main factor seems to be precision gunsmithing for maximum accuracy--with various platforms and cartridges.
Many folks here at THR "mess and tweak" with their own target and/or hunting rifles and achieve equal accuracy to anybody's "dedicated sniper rifle"--and no particular style of stock, scope, bipod, whatever is required.