Was ist der Unterschied zwischen write down und write out ?Du kannst auch einfach Beispielsätze geben.

When you "write down," it's like taking a note of it. There is no creative process involved. You can think of it like the difference between 쓰다 and 적다. If you write it down it has a feeling like 적다.

I wrote down the telephone number.
I wrote down what I needed to buy on a piece of paper.
I have trouble remembering things sometimes, so I write them down.

"Write out" is not very common in my opinion, but it means "to put into writing" or "to write something fully" like an abbreviation. For example, when someone "writes a song" it means that they come up with the lyrics, the melody, the chord progression, etc. That is, they compose the entire thing. If you "write out" a song it might mean that you are just writing down what the lyrics to the song are. You are putting the lyrics into writing. You could also be writing down a song that you are listening to, etc. Again, "write out" doesn't come up very often.

This usage of write out is more common I think:
When writing formally, you should avoid contractions and abbreviations and instead write out words fully.

There is also "write up" which can mean a few different things. It can be a more informal or colloquial way of saying "write" so you could talk about "writing up an essay on the history of Europe" in a conversation to a friend. This is also used when talking about reports especially. You "write up" a report. (But you can also just write a report).

The last use of "write up" is you can write up a *person*. If you write up somebody, this means that they have done something wrong and you are writing a formal report about it. For example, you can get "written up" for speeding by a cop.