Okay, that experiment shows me the relationship between current and resistance. But where in that experiment do I see the relationship between volts and amps? What would I change to represent volts, and what would I change to represent amps?

When someone says "current", they mean the combination of volts and amps, right?

Not if they're being at all precise -- in the language of electricians and physicists, current is measured in amps. Fuses, for instance, are marked with the maximum current they can take: those measurements are in amps. The complete mapping onto Genixia's experiment is:

Water pressure (psi) ~= Voltage (volts)
Water flow (pints/sec) ~= Current (amps)
Constrictedness of the hole (no sensible unit) ~= Resistance (ohms)

So increasing the head of water (which increases the pressure) is like increasing the voltage: it forces a greater current (more amps) through the same resistance (a greater flow through the same hole). To increase the head of water without increasing the flow (or increase the voltage without increasing the current) you'd have to make the hole smaller (increase the resistance).

Likewise, widening the hole will cause a greater flow for the same pressure: i.e. decreasing the resistance will cause a greater current (more amps) for the same voltage.

In other words, if you know any two of voltage, current, and resistance, you can work out the third. (And the same for water pressure, water flow, and "hole resistance" -- the only problem being that the relationship between "hole resistance" and hole size isn't very neat; factors such as viscosity and friction complicate it.)

The combination of volts and amps, since you mentioned it, is called power and is measured in watts. A high voltage at a low current delivers lots of power (think the jet of a firehose) and so does a low voltage at a high current (the Thames through London isn't going very quickly, but it'd be a devil of a job to stop it).

Peter