Voltage, also called electromotive force, is a quantitative expression of the potential difference in charge between two points in an electrical field. The greater the voltage, the greater the flow of electrical current (that is, the quantity of charge carriers that pass a fixed point per unit of time) through a conducting or semiconducting medium for a given resistance to the flow. Voltage is symbolized by an uppercase italic letter V or E. The standard unit is the volt, symbolized by a non-italic uppercase letter V.

Charge is merely the expression of a unit of matter (atom or groups of atoms) detailing the extent to which it has more or fewer electrons than protons. More, and it is negatively charged (or is said to have a negative polarity). Less, and it is positively charged (positive polarity). When two charged objects are brought into vicinity of each other, an electrostatic force develops (not to be confused with electromotive force, or voltage). If the electrostatic forces are of the same polarity, it is repulsive. If opposite, it is attractive.

Current is a flow of electrical charge carriers, usually electrons or electron-deficient atoms. The common symbol for current is the uppercase letter I. The standard unit is the ampere, symbolized by A. One ampere of current represents one coulomb of electrical charge (6.24 x 1018 charge carriers) moving past a specific point in one second. Physicists consider current to flow from relatively positive points to relatively negative points; this is called conventional current or Franklin current. Electrons, the most common charge carriers, are negatively charged. They flow from relatively negative points to relatively positive points.

Batteries and VDG machines both act as charge pumps. However, a VDG is different from a battery in one important way. Batteries produce constant voltage with variable current, while VDGs produce constant current with variable voltage. A VDG is similar to a battery, but the behavior of its voltage and current are swapped, and everything works backwards. If we short out a battery, we get an electrical overload. When short circuited, a large current appears in the battery's connecting wires, while the battery voltage remains the same. A VDG is the opposite: to overload a VDG you don't short it out, instead you run it open-circuited with no electrical load attached. When you overload a VDG you get a very large voltage, but the VDG current stays the same.

Batteries can produce large currents, while VDG machines can produce large voltages. A car battery is rated at 12 volts, and when a load is connected to it, the battery can create any value of current between zero and 500 amperes or so. A small VDG machine might be rated at 50 microAmperes current, and, depending on electrical load, can produce any voltage between zero and 100,000 volts.

The VandeGraaff machine is an excellent device for studying Electrostatics, the science of voltage and electric charge. Batteries are fine for studying electric current and circuitry. But if you want to investigate voltage alone, then get yourself a VDG electrostatic generator.

And from what I have read, Tesla coils are fascinating for creating high voltages as well, which dissipate into the air in the form of electrical charge. This is how the "electric plasma" glass balls operate in which bolts of charge follow your hand or finger as you touch the surface.

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