Writer vs Actor

What's the difference between an actor and a writer? Per Joan Didion, unlike an actor, a writer can perform alone - while an actor, even in a so-called one-man show, needs a director, a producer, a lighting designer, etc. Didion reportedly said:

I wrote stories from the time I was a little girl, but I didn't want to be a writer. I wanted to be an actress. I didn't realize then that it's the same impulse [...] It's performance. The only difference being that a writer can do it all alone.