You are correct. It is two waves canceling each other out.
If you imagine the sound wave as a shape that is flying towards you the noise cancellers generate the anti-shape one that when slammed together turns it into a flat line. (This is an oversimplification but enough)
It does this by using a microphone to pickup sound and play the inverse near instantaneously so they hit your ear at the same moment.
It is not perfect of course. But pretty amazing tech that requires well tuned components.
I don’t know if any headphones do it purely analog but theoretically it should be possible.
Heck you might be able to make a very crude version from off the shelf audio equipment and a custom circuit to make a speaker do active cancelling.
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