So i've heard the analogy of batteries compared to glasses of water to explain amps, volts, and watts. But what I'm curious about is weather batteries discharge as much and as fast as it can, like a water balloon expelling water, or is it drained by the circuit as it needs it, like a pump pulling water through a straw?

Closer to the straw. You can add multiple elements to choke the voltage or current. There is also things that can speed it up.

Different gauges of wire allow for different values of volts and amps as well.

The battery would be the balloon, the device would be a set of straws it pushes through to get to the other side, and complete the circuit.