Natural manaism is the belief that certain living things possess mana - and thus, that one can extract mana from them. However, generally it is understood that these same lifeforms are unable to use mana, and that only people can. Generally, smaller life forms hold less mana, and slower-moving (or nonmoving, such as plants) life forms even less still.
In its weak form, the belief is that certain living things, but not all, possess mana. The ones that do are generally animals, or higher animals only. (Remember, in its nonexistent form, the belief is that only humans possess mana.)
In its strong form, the belief is that all living things possess mana.