I worked in a indipend book shop for some years to help my best friend Elena in her shop. I met there a lot of published author (real "published author" 😁 ) and also some self published ones. Here in Italy we use to call "published author" a writer who was paid (signing an agreement) by a publishing house to publish a book, while we call "self published author" the one who had to pay to publish a book. Just to know, working on the book shop, I met also some people who called her/himself "a writer/an author" even if he/she has never published a book (that, for me, it's like to call someone "a professional photographer" just because he/she is the owner of a camera). :P