The word for "fall": taoreru vs. korobu (倒れる vs. 転ぶ)

倒れる "taoreru" is used for objects that fall down while stationary. Therefore, this is used for inanimate objects and for people who collapse.

転ぶ "korobu", on the other hand, is used for objects that fall while moving, so this is used for events like slipping while skiing or skating.

Reference:
Akira Miura, Essential Japanese Vocabulary, Tuttle