What physically determines what voltage something has? I know that voltage is energy per charge / energy per electron, but since something such as a wall outlet has 120V with a lot of current but a mostly harmless low current Van De Graff generator has 100kv with almost no current, what factors actually determine how much voltage something has? It seems like if you are producing high voltage you would also produce high voltage and the other way around, since more energy means more current, but this does not seem to be the case.
 A: A good way to think about voltage and current is a "plumbing analogy":  a wire (or any conductive path) is like a pipe carrying water.  Voltage is like the pressure difference between the two ends of the pipe.  Current is like the amount of water flow in liters per second.
In the case of a Van de Graaf generator, there isn't even a wire; there is only air.  The air is an excellent insulator, something like a pipe that is plugged solid.  In the Van de Graaf generator, voltage keeps building up until the air becomes ionized and conducts a spark.  By analogy, with enough pressure difference, the pipe will explode and water will spray everywhere.  The reason the spark won't kill you is because it really doesn't take very much charge to build up a high voltage, so the discharge is brief.  The amount of energy delivered to you (volts x current x time) is quite small. The charge on the Van de Graaf sphere drops extremely rapidly because the current depletes the charge much, much faster than the belt in the generator delivers charge to it.  The voltage difference between the sphere and anything that's grounded is directly related to the charge on the sphere, so when a spark jumps from the sphere, the voltage difference drops to almost zero -- then gets built up again relatively slowly.
The reason the wall voltage of 120 volts will kill easily is because the wall outlet will supply an effectively unlimited stream of current up to 10, 20, 40, or more amps, with no drop in voltage.  The amount of energy delivered to you from the wall outlet can be much, much more than the amount delivered in a spark from a (small) Van de Graaf generator
A: What physically determines voltage, is electric field.   Electric field is defined as electric force (not electrodynamic,  however: we must
exclude changing magnetic fields for this to work) per unit of charge,
and has both a magnitude and direction that can be determined, theoretically, by tossing a small charged 'test particle' in, and watching
its acceleration.
The absence of changing magnetic fields makes an electric field mappable
in such a way that it has a vector value at all points, but has
no curl at any point.   Such a field can be simplified from 
a vector field to a scalar field (which has a numeric value
at every point, but no direction) and the 'gradient' operation.
$$\nabla V = \bf{E}$$
So, the electric field E (vector field which has physical reality) can be 
equated to the gradient of a voltage (scalar field V), which
is not a real thing at all, just a mathematical construct.
To be correct, any scalar field that has the right gradient
would be acceptible, and that means one can add an arbitrary
constant to each point of any voltage field; a constant
field has zero gradient, so it doesn't change the resulting E field.
A voltmeter measures differences between two probes, so it
has a little more physical reality than 'voltage', because
that cancels out the arbitrary constant, but no voltmeter
gives meaningful measurements in the presence of fast-changing
magnetic fields (because the curl of the E field doesn't 
vanish then, and that invalidates the construction of V).
