Jerk is the third derivative of position and is very familiar to anyone who has ever ridden a bus or other vehicle with not-so-smooth acceleration curves.
An interesting fact: it has been shown ([0], [1]) that human body movements are performed in such a way as to minimize the jerk, so the jerk is used in robotics to make humanoid robot movements look more natural.
Intuitively I think you would be able to tell the difference between a jerk and a snap. In a car experiencing jerk, you would find yourself no longer able to balance against acceleration and you would sway. In a snap, you would not just sway, but really bounce around. Think the difference between hitting the gas pedal in ludicrous mode vs hitting the gas pedal while driving over potholes.
Crackle and pop, I have no idea if you could tell the difference.