I think of power through a cable as water through a hose:
Water is a very popular and well worn analog for electricity.
Voltage is the "pressure" of the water (like a garden hose with a fine mist head on the end of it (Hi Voltage)versus just being open and the water dribbiling out(Low Voltage)).
Yes, kind of... Water pressure is analogous to electrical potential... voltage is the pressure that pushes current through the wire. However your example of an open and closed hose nozzle are examples of how different impedance or resistance, and current capability react.
The hose is like a speaker wire, and the nozzle setting is like a high impedance or low impedance speaker load. With the nozzle almost completely closed off (think 600 ohm headphones ) current flow (water flow) is low, and the voltage (pressure) in the hose remains high. Alternately if the nozzle is wide open (2 ohm load), the flow (current) is much greater, with water pressure (voltage at the end of the wire) much lower.
Amperage is the size of the hose (think potential here: is the hose a straw or a 12" conduit? This has nothing to do with the actual amount of power being drawn through the hose).
Amperage is directly analogous to the amount of water flowing through the pipe. The size of the hose is more analogous to wire resistance. Heavy gauge wire is like large diameter pipe. Just like getting good current flow to speakers is improved by thicker wire, wider pipes will get more water flow to your shower from the same water pressure.
Wattage is the actual amount of water. Obviously you can get more water through a bigger hose. A fire hose going full tilt would be like 400A, 600V. Sipping water through a straw would be more like .5A, 120V.
bzzt.. amount of water (flow) is current, amount of still water is like charge sitting in a capacitor.. big capacitor, holds more water, capacitor filled up has more potential pressure (voltage).
Power does not fall out of the water analogy very neatly. The work (and heat) associated with a water pump is similar to power because it is directly related to flow (current) and pressure (voltage) of that water being pumped. I.E. Low flow and/or low pressure is easier on the pump than both high flow and high pressure at the same time.
I would re-label the cartoon so that the pipe was the Amperage and the character getting the squeeze is the Wattage.
The cartoon is actually quite good as is.. pipe diameter is resistance so making the pipe smaller increases resistance and restricts flow. Current is the amount of flow, and voltage the pressure pushing the current. The real Mr. Ohm is not turning over in his grave.
Mr Watt may be harder to please. Power is harder to describe with literal images since it is the product of two linear characteristics, so a nonlinear product.