400KV from Van De Graaf VS electrical transmission lines: breaks ohms law?

Ohms law dictates that voltage and current are always related. You increase or decrease either, the other will always follow.

How is it that an electrical transmission line at 400KV carries so much more current than a VDG spark? (the VDG feels painful whereas the power line kills)

I just found this youtube video:

looks like it basically answers this question. is my below understanding of the video correct?

a statically charged balloon or a VDG pumps very little energy into you in one brief moment. it's a combination of the body's ohms + body picofarad range capacitance.

a 400KV electrical power line however is a continuous voltage source that will pump killer amounts of energy into you non-stop.

Of course voltage and current are inversely related by Ohm's law for a fixed resistive load, but they are not locked together if the load changes. You can have either high or low voltage at either high or low current. A Van De Graff generator provides a high voltage at low current. A power generator provides high voltage (through transformers) at high current.

It is a combionation of more factors, but you got it pretty close. A VDG has very little energy stored in it, so the length of the pulse is very small, so even though the peak current could be high it last for a very short time, so it is not too dangerous.
A 50hz 400kV line is a different beast - the energy it can deliver is practically unlimited, so the only thing that limits the current is the resistance of your body. And with the numbers being what they are there could be tens or hundreds of amps flowing through you until your're burnt to a crisp, and the distribution site wouldn't even notice something is happening.
In a picture tube the capacitance is much higher, so the energy stored will be higher so the pulse would last longer which is another factor that would most likely kill you.