You're only a writer WHEN you're writing.
Like when you're at your desk at your keyboard writing the words. Then you're a writer.
At other times maybe you're making notes for your writing, then you're planning to be a writer. Or you're editing your writing, then you're an editor.
Or you're at a cocktail party and someone asks you what you do for a living and you say, "I'm a writer." At that moment, whether you want to or not and whether you can admit it or not, you're not a writer: you're a status-game player.