i have this personal measurement of what makes an "author" and a "writer"
to put it succinctly, an "author" is like an A24 movie while a "writer" is more akin to hallmark drama production. the two aren't mutually exclusive but it's rare to see them overlap.
to put it in harsher words, an "author" would write something like Catch 22, or Catcher in the Rye, while a "writer" would probably make another Jack Reacher/Alex Cross entry
Sometimes you'll get a combination, like the Harry Potter series.