There is no current without voltage, what you're saying makes no sense.

Current is voltage over resistance, you get as much current as you have voltage, unless there's an artificial effect limiting voltage, like a voltage regulator or zener diode or just fet.

When you say 'it's the current', that electric fense has x volts before you touch it, and the fact that it doesn't kill you means either the voltage is too low to produce a decent current in your body, or, there's a voltage regulator/limiter that means when you touch it the voltage drops to some lower level, which I could calculate using the nominal resistance of the human body and the voltage of the fence.

In a way, the output impedance of whatever is driving the fence determines how much the voltage drops under load.

I'm speaking about the voltage needed to get the deadly current across the critical areas of your body BTW, which can be handled as a kirchoff circuit I'm sure.

In most household shocks, you touch a conductor, and you are the resistor to ground. Your resistance is independent of the drive voltage, so if you touch a 110V wire, the current will be half of what you get with a 220V wire. So the voltage determines the current, and thus the lethality.

There’s lots of other factors that go into the effective resistance like the amount of moisture on your skin, what shoes you’re wearing, and what the floor is made of, etc, but in all cases twice as much voltage will cause twice as much current. You are by far the highest resistance element in the circuit, so your resistance will completely determine the current - most household circuits are capable of supplying 10-15A continuously, so your resistance is the current limiter.

It’s a bad idea either to go touching live wires either way, but the rule of thumb I heard was was that a 110V shock usually won’t kill you and 220V shock usually will.

No it's not, I'm an ee.

P = I^2R, so power squares against the current, while it's linear to voltage.

This means current causes more heat dissipation in the wire, which has risks, potentially fire if you really go too far, this is why breakers trip.

But what really causes fires (again, outside of crazy overcurrent) is Arcing, from basically either bad connections or bad insulation, OR, from an inductive load that gets disconnected, so the current tries to stay constant in the coils, which leads to massive voltage spikes.