word difference - Fall vs Fall down

I can't know the difference between "fall" and "fall down", I saw both definitions in Cambridge and in some dictionaries, but they seem to be the same to me.

See these definitions:

Cambridge Fall - to suddenly go down onto the ground or towards the ground without intending to or by accident.

Cambridge Fall down - to fall to the ground

Cambridge Fall vs Fall down - We can use fall as a noun or a verb. It means ‘suddenly go down onto the ground or towards the ground unintentionally or accidentally’. It can also mean ‘come down from a higher position’. As a verb, it is irregular. Its past form is fell and its -ed form is fallen. Fall does not need an object.

*We can’t use fall down to mean ‘come down from a higher position’:

House prices have fallen a lot this year.

Not: House prices have fallen down a lot …*

What does it mean? Why is it not allowed to use fall down when something comes down from a higher position? If something falls down, according to the Physical laws, the object had to be in a higher position, if not, how did it feel "down"? It doesn't make any sense to me, how can something fall down without being in a high position?

Can anyone explain to me the difference between these two terms, because I read it many times but I still don't get it, as far as I'm concerned, it may be optional.