Electricity tends to kill you in one of two ways.
The first way is that it screws up your heartbeat, and for this it does generally have to pass through your heart. If you hit the heart with a jolt of electricity, it can get its rhythm all screwed up and it goes into what is called “fibrillation”. Instead of beating in a nice normal rhythm, it just kinda sits there and shakes somewhat chaotically. The human heart has kind of a funny design where thef fibrillation state is stable. In other words, if you can get the heart into fibrillation, it will stay in fibrillation and won’t come out of it on its own. Since it is not effectively pumping blood, you pass out fairly quickly and die soon after that from the lack of blood flow.
It takes a surprisingly small amount of current to potentially screw up your heartbeat. Most safety standards (in the U.S. at least) are built around 5 mA (0.005 amps) being the “safe” amount of current. Below that, the danger of fibrillation is so small that it’s not worth worrying about. By the time you get up to 100 mA or so (0.1 amps) the chance of putting the heart into fibrillation are pretty good. The thing is though that this is all rather hit and miss, so there’s an awful lot of luck involved. The way our heart is designed, it is much more sensitive to being thrown out of whack at certain parts of its rhythm than others, so if you get an electric shock at one of those points in the heartbeat it is much more likely to go into fibrillation. At other points during its heartbeat cycle it is much less sensitive to disruption, and much less likely to go into fibrillation.
At first, the more you increase the current, the more likely you are to go into fibrillation and die. But then a funny thing happens. Once you get enough current, the heart muscles all just clamp instead of going into fibrillation. At that point the heart still isn’t pumping blood, so if you don’t end up being separated somehow from the source of the electricity you’ll still die. However, if the source of current is removed, the heart will usually go back into a normal rhythm.
But then as you increase the current more, the heat generated by the electricity flowing through you starts to cause burn damage, and the fatality rate starts to climb again. This is the second way that electricity tends to kill you. It literally cooks you to death. This requires much more current, but it’s much less hit and miss. It also doesn’t necessarily require the current to go through the heart.
When you do something like drop a hair dryer into the bathtub, the most likely cause of death will be fibrillation. The electric chair and lightning both tend to kill you by cooking you to death. Lightning is very hit and miss simply because the voltage and current are both so incredibly high that it behaves in very weird ways. At those extreme voltages, things that aren’t normally considered to be electrically conductive (like, say, a few miles of open air) all of a sudden become conductive paths for lightning. So there’s no telling what path the lightning will take as it goes through you. It may fry your internal organs and kill you. It may travel more along the surface of your body and just cause you some severe burn damage to some of your muscles. If the bolt splits and only a tiny fraction of it goes through you, then you may end up rather shaken from the whole experience, but no real harm done.
As was already mentioned upthread, lightning can kill you in other ways, too. If lightning hits the ground nearby, you may have a few million volts where the lightning hit and zero volts on the other side of you (earth potential), with the voltage kinda spreading out away from where the bolt hit. This means that you could have a few thousand volts difference between one foot and the other, causing the electricity to travel up through one leg and down through the other. Lightning contains a tremendous amount of energy, and that energy can do things like boil the sap inside of a tree, causing the tree to literally explode. You can be killed by fragments from the tree or falling tree parts if the tree comes completely apart.
The human body’s “resistance” to electricity is not a simple thing. At relatively low voltages, like that of a car battery, the body’s resistance is pretty high. A multimeter, which uses a very low voltage to measure resistance, will often read several hundred thousand ohms or higher. At higher voltages, the human body’s resistance drops down to maybe a thousand ohms.
What this all means is that lower voltages are generally not harmful to people because they can’t overcome skin resistance. You can touch both terminals of a battery and you won’t get shocked. Once you get above 50 volts or so though that’s no longer true. As the OP noted though, you still have to be careful with batteries that have a large current capacity (like a car battery) as accidentally shorting the battery with something that is conductive, like a wrench, can cause a huge amount of current to flow. Not only can the wrench overheat and melt, but the electrolyte can overheat and boil, causing the battery to explode. Having a battery blow up in your face is no fun.
A tiny jet of water through a microscopic orifice at 100,000 psi can cut through a plate of stainless steel or a block of marble.
