So while high current does kill you, what causes it is high voltage. What is considered high? Depends on your impedance (ex. are your hands sweaty or dry?).
When dealing with high-current systems, there are safety procedures and concerns, but they are generally different than high-voltage. The systems I have dealt with are more about burns than electrocution. For example accidentally shorting out a fork lift battery can be spectacular in a bad way.
1,000 Amps and 5 volts is dangerous (sort of), but not in an electrocution sense.
Despite the fact that you’re experiencing the same gravitational acceleration from both, a one meter fall, while being potentially dangerous if you’re not prepared and allowed to land right, is not likely to kill you. A 100 meter fall, on the other hand, is likely not survivable by any means.
So the reason high voltage is more dangerous, if it has sufficient amperage backing it up, is that the higher the voltage, the better its ability to pierce your skins resistance and flow through your body to begin with.
High voltage is inherently dangerous.
If you do this in a vacuum you could get X-rays, and if you do it near your cellphone or laptop you can kill them. But it's not dangerous to your body.
However, high voltage with enough power behind it to burn a Lichtenberg figure through your body can kill you pretty darn quick.
The risks with low voltages and high amperages are from shorts causing rapid heating.