I looked this up earlier and found some interesting takes on this. Traditionally, the word 'author' has been used to indicate a person who has written a book (usually but also can be for articles) that has been published. The word 'writer' is simply used for a person who writes (any subject and any media format).
I think if you call yourself a writer or an author, you care to write. Today there are many people who have books ghostwritten so technically, they would not be real authors. They would just be buying the works of other writers. Perhaps they had authored the concept. Today you can also self-publish and you can create your own works in electronic format easily. The words 'author' and 'writer' are being used interchangeably today.
The way I look at it, both authors and writers are engaged in the craft of writing. To be effective in any art form, you have to practice it enough so it is fresh for you and you can focus on the substance rather than the format.
I consider authors to be a subset of writers - people who have published works under their own name or pen names. To understand the word 'author,' I went back to the origin in Latin 'auctor' or 'augere,' which means to 'originate, increase or promote.'
That is so insightful! My takeaway from this is that being an author means you are creating your own work that you promote. That's the primary distinction I take between the two words. I think it is empowering to be an author. You are exerting creative control over your own work that you decide to create and write.
I think it is quite fun and liberating with endless possibilities...