Paul falls off his bike, and Michael falls from the tree.
The uses are not exactly the same, because while 'fall from' can be used in most cases, we can only 'fall off' things that we get on (or get onto).
So Paul can fall from his bike, but Michael cannot fall off a tree. However, Michael can fall off a branch of the tree, as he can 'get on' a branch but not 'get on' a tree.
The reason we can use 'fall from' more widely is because 'from' only says where the object started, not whether it was on or in that place. So (for example) rain can fall from the sky, but not off it.