Voltage is just a mean to apply current. Professors used to tell us that we're just a bunch of 1kΩ resistors, but actual resistance depends on conditions like wear, type of skin, humidity etc.
If the voltage is too low then you cannot apply high enough current. So high enough voltage is a condition but not a guarantee. Guarantee is high voltage with provided current. Good example of safe high voltage is static electricity - the overall electric charge is very low, so despite extremely high voltage, the current produced is minuscule and all it does is maybe sting a bit(or destroy electric equipment).
Now if you have high voltage source which can provide high current, then you're getting in trouble. Hight current with enough exposure time is what causes the danger. Here's a chart showing how long you can stay safe with certain current flowing through you, this particular one is for AC in frequency from 15Hz to 100Hz:
Keep in mind that this is for AC. For DC current, the thresholds are generally 2-4 times higher.
Anywhere in AC-1 area is completely safe(for people without cardiac problems or pacemaker) and generally barely noticeable.
AC-2 is still safe but not recommended, and generally lets you set yourself free from the source on your own.
Anything above is potentially fatal. Line b marks the end of area where you still have control on your body and can potentially deattach yourself, anything more means you need help.
AC-3 marks an area where there are very likely pathophysiological symptoms such as muscle contractions, problems with breathing, cardiac disorders etc. Still not fatal but really dangerous and the longer you stay the higher possibility of long term damages.
AC-4 is pretty much guaranteed one or many of the following: respiratory arrest, cardiac arrest, burns, and the higher you get, the higher % probability of Ventricular fibrillation. 1A has a 50% probability of VF. AC-4 pretty much means near-certain death if not helped in an instant.
Aside from the pure reaction of your body, there's also an aspect of surroundings. If you happen to be on a ladder, then even AC-2 can suprise you enough to make you jump back and cause a dangerous fall. AC-3 is very likely to cause muscle contractions so it can literally sweep you off your feet and make you lose your balance, again causing another type of danger.