In 1909 when Hiram Maxim put the first modern baffle-type mufflers on a gun barrel, he called them "silencers" and incorporated the Maxim Silencer Company, Hartford, CT. "Supressor" is modernist jargon.
Accuracy: I have seen supressed .308s being shot at 1000 yards. Accuracy was comparable to my straight barrelled rifle. Noise level was still high enough that ear protection was needed. Remember, even though the muzzle blast is advertised to be brought down to .22 level, that is still well over 100 dB. The whistle as the "can" depressurizes from trapped powder gas is distinctive.
Shock wave: I don't know if it is the muzzle blast from 1000 yards or the shock wave as the bullet passes over, but I definitely want ear protection in the target pits of a formal range.