you're thinking of like, being choked, i presume. the difference is that choking directly cuts off bloodflow to the brain, but if the bloodflow isn't disturbed then there's a decent bit of oxygen stored in the air in the lungs and in the blood itself.

this is how animals like whales can dive for hours at a time, they store oxygen in their blood.

The thing that actually makes you feel the need to take a breath is buildup of CO2, not lack of oxygen. My understanding is that holding your breath isn't really about the amount of oxygen you have but rather how long you can resist the urge to breathe, though presumably at these extremes they do have to pay attention to how they feel and abort if they start feeling tired or whatever low oxygen does to you.

i remember reading that divers actually have some form of brain damage