Now that it's getting close to Halloween, we're running a contest to hear your scariest stories! These can be scary stories that you've experienced or stories that you've heard and the story with the most reactions will win!
Voltage is the electrical potential. It is measured in volts, of course, which are joules per coulomb (J/C). So it is a measure of the energy per unit of charge.
Amps is the unit for the current that is actually running through an electrical circuit. Its constituent units are coulombs per second (C/s), so it is a measure of the rate at which charge is flowing. A high amperage (current) means a lot of charge running through the circuit that is carrying a certain amount of energy (how much depends on the voltage).
Note the famous equation P=IV. Current (C/s) times voltage (J/C) equals power, which can be measured in watts (J/s).
Skin is very poorly conductive, so you need a high voltage for actual charge transfer. Heart tissue is maintained over a very small range of membrane potentials (-70-10mV) so large current would cause severe depolarization and subsequent cardiac arrest.
The voltage is not directly important - what matters is the current and for how long it flows. Certain minimal current needs to flow through your heart for a certain period to kill you - we are talking about milliamps of current and seconds of time. The ways to stay safe are either by limiting current or the time of discharge. I don't know what exactly the current from cattle prod is but I'm willing to bet that it is applied only for a very brief moment. In that case what makes it safe is more related to the duration of the electric shock.
Also, it's very bad idea to think that volts will not kill you. With the same application points and with no limit of the charge, higher potential will be more dangerous (and will lead to higher current).
Sorry, didn't mean to sound like I was talking down to you.
But, really, if you already understood what I said, then there shouldn't be a question of volts vs. amps killing you. The two are intertwined. Volts are the potential to deliver energy, while amps are the "vehicle" of delivering said energy. The following is straight from my physics textbook:
"The seriousness of a shock depends on the applied voltage and on the effective resistance of the body. Living tissue has low resistance since the fluid of cells contains ions that can conduct quite well. However, the outer layer of skin, when dry, offers high resistance and is thus protective.
Most people can "feel" a current of about 1 mA. Currents of a few mA cause pain but rarely cause much damage in a healthy person. Currents above 10 mA cause severe contraction of the muscles, and a person may not be able to release the source of the current. Death from paralysis of the respiratory system can occur. If a current above 80 to 100 mA passes across the torso, so that a portion passes through the heart for more than a second or two, the heart muscles will begin to contract irregularly and blood will not be pumped. This condition is called ventricular fibrillation."