Here's a simple kitchen experiment that may help you to really get a grasp; Get an old soda bottle or clear juice bottle, about 2L is ideal.

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? In all these analogies, you guys keep saying "current", and I'm looking for a way to grasp what the two different halves of "current" represents. I haven't yet seen anything in the water analogies that shows me this. To me, it's all the same. More water= More pressure, even in the soda bottle analogy. So in that analogy, if the height of the water represents volts, then what represents amps?

Sorry if I'm being dense. These are all very good and detailed explanations, and I really appreciate them. Everyone is really giving it their best shot, and my puny brain is still not seeing the difference between the two...