am I a writer?

small boy asks sleepily, "What are you doing Mama?"
"Writing," I reply.
"But why, Mama?"
"Because that's what Mama does, baby, Mama writes."
"Oh, I get it," the precocious little guy says, though his tone tells me he isn't quite sure.

Is there a difference between merely wanting to be a writer and actually being one? Do I need readers to be a writer?

Maybe I need a thesaurus.