What is the difference in the physiological mechanics for a knockout caused by an impact to the head and a knockout caused by an impact to the liver?
Head shots - knock out
Impact to the head can cause actual loss of consciousness, by brain trauma.
Liver shots - knock down
Hitting the liver can be devastating, but does not cause loss of consciousness. As shown here in the Hatton/Castillo fight, or here, with de la Hoya getting hit by Bernard Hopkins, liver strikes can be so incredibly painful that even hardened fighters will give up--turning away, taking a knee, writhing in pain--but nobody passes out from them.
Even when Bas Rutten hit Jason Delucia in the liver five times, rupturing the organ, nobody passed out. Jason is just stunned and collapses from the enormous amount of pain.
My understanding is that it is somewhat easier to hit the liver with smaller gloves or no gloves. For this reason it is a popular target in Kyokushin karate, as seen here:
For further information, I recommend this overview by two doctors, in the context of muay Thai, self-defense, boxing, and mixed martial arts. They contend that strikes to the liver are the most debilitating out of any target on the body (excluding the head).