Great analogy; I've used it myself at times. I think you got the voltage/current thing reversed, however.
Voltage provides the "push" or pressure behind the flow of water; current, in amperes, is like the diameter of the pipe. A big pipe, like a firehose, enables a big flow of current. A narrow pipe restricts the flow of the water.
Big fat wires like jumper cables carry tons of current "pushed" by a low voltage (12 volts in a car).