People often mistakenly consider writers and authors as synonymous. They are not. They are closely related, and one might even suggest that the concept of writer is nested in the concept of author.
Many people are writers who are not authors while everyone who is an author is a writer.
A writer is anyone who engages in writing on a regular basis, either for their own personal enjoyment or as a profession. For example, a person who journals is a writer. So also is a newspaper or magazine columnist. They are not authors in the sense a book writer is however.
I believe that there are three criteria for being recognized as a 'legitimate' author.
First, you must have written a book,
Second, your book must have been published.
These two might be considered sufficient to qualify someone as an author, but I think one more element is required for the public at large to consider someone a 'legitimate' author.
That third element is that someone has actually purchased your book.
I have had the good fortune to have realized all three. This was the realization of a long held dream.
I became an author for three reasons.
Number one was in order to fulfill a promise I made to myself a long time ago.
Number two is that I believe I have something of value to share on a wide variety of topics, and feel a sense of obligation to do so.
And third, I would like to earn a significant living from my writing.