I think you've pretty much got it yeah :) The "Water Analogy" as it's called only goes so far really.
Amperes, in this situation I'd say is the "flow rate" of the water.
Some people even push this analogy a bit further and suggest that say a water-wheel (that water sets spinning and then has some inertia) could be compared to inductance, or that a stretchy section of pipe could be seen as capacitance too.
Something I found interesting working with our Chinese counterparts in electronics design at work is that they often translate Voltage to "pressure".