A writer is a writer regardless of capacity. A writer can earn a living with writing alone, but a person who writes while earning a living doing something else is just as much of a writer. Take Nobel laureate Toni Morrison for example:
“Morrison began writing fiction as part of an informal group of poets and writers at Howard University who met to discuss their work. She attended one meeting with a short story about a black girl who longed to have blue eyes. She later developed the story as her first novel, The Bluest Eye (1970). She wrote it while raising two children and teaching at Howard.”
Often, there’s a misconception about having to identify yourself with what you do for a living. One can certainly do this – my friends who are utilizing their vocation as their main source of income generally identify themselves with their jobs or careers – but it’s not always the case. I’m currently not employed as a writer, yet that is my vocation. (I’m not even that good, lol, but I know I must.) Essentially, I believe a vocation is a calling that one can and should commit to to experience maximum fulfillment in this life and of thyself.