The suppressor is an attachment attached to the mussle of firearms to suppress the mussle flash of, and limits recoil a weapon. Where as a silencer deafens the sound of gun shots and can reduce the mussle flash. Both are used in used in a few GTA games but comes standard on most weapons and cannot be removed.
The silencer first appeared in Grand Theft Auto 2 on the Silenced Machine Gun. The silencer's only purpose is to make pedestrains, inluding cops, oblivous to to the gunfire.
In Grand Theft Auto: Vice City the suppressor appears on the PSG-1, though it serves no purpose other than athstetics.
In Grand Theft Auto: San Andreas the silencer appeared on the Silenced 9mm. The silencer serves the purpose of stealth, as firing the silenced 9mm will not alarm any pedestrians, unless the pistol is pointed directly at them, nor will it attain you a wanted level, unless fired very near a police officer.
In Grand Theft Auto: Vice City Stories the silencer appears on the Mac 10, though it serves no purpose other than to make pedestrians and cops oblivious to gunfire.
The suppressor makes appearance again in Grand Theft Auto: The Ballad of Gay Tony but this time on the Assault SMG. Unlike previous games, the suppressor serves no purpose other than to supress the mussle flash the weapon.
A silencer/supressor Grand Theft Auto V it is seen on a Type 56 variant of an AK-47 in the trailer.