This is also the difference between what are known in mixed martial arts as 'air chokes' or 'blood chokes'. An air choke does just that, cuts off the ability to breathe by compressing the trachea. Certain positions with a guillotine choke do this, along with the gogoplata (shin choke). You can also do this with a rear naked choke, which was how PRIDE veteran Fedor Emelianenko preferred to use the hold.

A blood choke compresses one or both carotid arteries and blocks bloodflow to the brain. Properly applied, with enough strength and leverage, a blood choke will make someone pass out in about 5-6 seconds max from hypoxia (lack of oxygen to the brain). Blood chokes are used more often in combat sports precisely because they're much quicker.