Each organization has its own separate rules in regards to the safety of the competitors. In boxing, once you fall on your knees, it counts as a knock down and you will get a count along with the question of being able to continue by the referee. In amateur boxing, you also get standing 8 counts if you get rocked.
This factor is missing in MMA, where grappling and ground game is allowed. Competitors are allowed to pummel their opponents as they fall down to make sure they are really out. In addition, bleeding is not a big issue in MMA. They are allowed to continue unlike in boxing, where profuse bleeding may end a match.