I teach 2nd grade, and I do not use a writer's notebook. I've found that the lines are too narrow for many kids, so I use a writing binder. I have several paper choices, and they choose which kind they would like to use. My binder is divided into 3 tabs: finished writing, unfinished writing, and tools. They can continue their writing from writer's workshop during Daily 5 time, or they can do something different. For example, during writer's workshop we are focusing on personal narratives. However, during Daily 5 they can make lists, write an informative piece, a story, etc. All of the writing is stored in their binders. I think that if it were separate, they may not connect and apply the skills they're learning during writer's workshop during Daily 5 time.
I do have a math notebook and a separate reading response notebook.