Usually, when someone says “write something out” they’re talking about writing down something that someone said, something they saw, or an idea they had. As in, changing the form of something (an idea, song, movie, etc.) to being in written form. Ex. “I just thought of the best business idea! I need to write this out” To say “to write something” just means to write a story, essay, sentence, review, etc. Basically, to write literally anything. Ex. “I’m bored, I’m going to go write something” I hope this helps!