Amplifier circuitry-4 ohm vs 8 ohm

Obviously there are different wires leading into the four or eight Ohm taps on the back of an amplifier from the one amplifier.  The single amplifier at some point splits the signal going into either one of these Ports.  What differences are there in the circuitry?

Maybe this will help me better understand the difference between these two taps. I believe 4 ohms is a wider more open path for voltage to flow. So when you're speaker attempts to go lower, which requires more power, the 4 ohm more easily allows this to happen with a better outcome. Or maybe I got this wrong.