Jerk, snap, twitch, yank mean to make a sudden sharp quick movement.
Jerk implies especially such a movement that is graceless, forceful, and abrupt.
Snap may imply a quite quick action abruptly terminated (as a biting or trying to bite sharply or a seizing, clutching, snatching, locking, or breaking suddenly) or a taking of possession with avidity or sometimes specifically an uttering with the brisk sharpness of a bite.
Twitch may imply quick, sometimes spasmodic, and often light action combining tugging and jerking.
Yank implies a quick and heavy tugging and pulling.