Let’s have a look from the point of view of a non-native speaker. One of my clients, working on presentation to piano students, asked me this:

“Write down your fingering, write in your fingering, write out your fingering.

Are they all different?”

Well, oddly enough– and English can be very odd at times– in this context they are almost interchangeable. Sure, there is a slight difference- to write something down means to get it on paper, to secure it, where writing it in is putting it in the correct place, and writing it out means getting it all there from beginning to end- but as an instruction to a student, any one of them works. “Writing in” is preferable to “writing out” and “writing down” in this case, but really not by much. However, if you were to ask someone to go to the store and get a list of things, you would say, “write it down”, where if you need the exact wording of something, with no shortcuts, you would say, “Please write it out.” “Write it in” is adding something to an existing text, whether it’s a form, a paper you’re notating, or a piece of music.

It’s fascinating to see how many of our wording choices are unconscious. They seem obvious to us, but to an English language learner they are a major headache. And even in my writer’s group, I see a fair amount of confusion on some of these little distinctions. That’s one reason why having a second pair of eyes on your writing is always helpful!