They are very close and can be used interchangeably in MOST cases. I would distinguish a directional difference. Fell over (or fell down) can be used for something that just turned on its side. "The bottle fell over." "The display fell over." Fell down can mean the actual direction. You would say someone "fell down the stairs" but you would never say they "fell over the stairs."

They are similar, in fact I would say they mean the same thing ( to an American). Fall can mean that something failed as well. The fall of the Roman Empire for example means the collapse or end. For the most part, fall and fall down means the same thing.