So, does a 4-ohm speaker play louder than an 8-ohm speaker with the same amplifier and volume setting?
It's entirely dependent on speaker's sensitivity and output level, which is usually measured at 1 m.
On the other hand, an amplifier will output more power with lower impedance.
Here's the output of Hypex NC400:
580 watts at 2 ohms
400 watts at 4 ohms
200 watts at 8 ohms
If you were to measure a speaker with DC you'd get a resistance. If you were to measure it with AC at various frequencies, you'd get impedance.