'fall from' ... a place, you have to mention the starting point of the fall. 'fall off' specifies a sudden and heavy fall without necessarily stating the starting point.

We tend to use "fall from" when the point of origin is specified, rather than general. Examples: The politician fell from his position of absolute authority. "Off" wouldn't work here at all. The cat fell off the roof. The cat fell from the tree branch. but... The painter fell from the roof. The painter fell off the roof

He fell off his chair. =(he fell off an object) He fell from favour. = (he fell from a higher status to a lower status)

Consider them the same. They are interchangeable; although, if you are not actually on top of something, then only use fall from. These two sentences He fell off the building. - Here he was at the very top of the building. He fell from the building. - Here he may have been on top or at any story (assuming a multi-story building)