Any question answered...

Yes, even if they are using the same driver circuit (and they probably don't in your example), the impedance varies between speakers, and the volume knob just varies the output voltage. Power drain is inversely proportional to speaker impedance, so switching from 8Ω to 4Ω speakers will double power drain at a given output voltage, assuming the amplifier's internal impedance is negligible.

tru dat yo, but amplifiers don't have a negligible internal impedance (hence "impedance matching", where you match the impedance of your speakers to the impedance of your amp to maximise power transfer)

So some types of speaker drain a device more than others regarless of the volume set on the device ?

Think of it this way; there are two ways speakers/headphones dissipate energy: heat (electrical resistance in the wires) and kinetic energy (noise). Assuming the headphones/speakers have been designed fairly well, we can ignore heat. A speaker makes more noise (it can be heard from further away) so it is using more energy than headphones. But, headphones can sound louder because you're much closer to the source of the sound (and it's more directed). So Headphones are more energy efficient.

When I say headphones, I'm assuming small, in-ear things.

But without running some tests it's difficult to say. I'm no expert.

Ciao!