The diaphragm material, speaker size, speaker magnet, and speaker coil all contribute to the performance of a headphone's speaker.

It's difficult to say why a speaker has a specific design or uses a specific technology - audiophiles can only speculate.

Only an engineer or someone who studies the subject can make definitive statements, but explaining it also involves understanding the mathematics and physics of audio.

Acoustics also plays a part in the performance of the headphones and are related to the speakers.

Finally, the entire construction of a headphone is related to the acoustics of your ears, whether it's the acoustics of the outer part of your ears (pinna) or the acoustics of the inner part of your ears (auditory canal).

All of these factors are synthesized in what is called the headphone frequency response graph (the most useful information for us as consumers) and THD.

Regarding the analogy between headphone speakers and cars, it is not a perfect analogy. It is possible to make good headphones with speakers that can be considered inexpensive.

Regarding "speed" in headphones, mathematically speaking, the idea of speaker speed is not very interesting since the frequency response can be derived from an impulse response. So if the headphone can reproduce frequency X at Y dB with no distortion, that's what it does.

The idea of attack speed can only be understood as something derived from the auditory perception of the frequency response of the headphone in your ears. I recommend that you don't place too much importance on the term "speed or attack speed," as each audiophile may have a different interpretation of what it means. It's a language game.

If you want to know about some of these terms, I recommend this here.