This is my opinion for what it's worth.
It does seem that people will vacillate between describing themselves or others as a writer or author. Does it matter? We do like labels even if @JamesSavik (where have you been by the way) might say that 'labels are for cans'. And there's a fair amount of back and forth on the internet about the subject. But I personally count someone who writes original ideas in story formats and accomplishes this with even a modicum of ability, who continues to hone their craft, and puts their work out for others to read (however that comes about) can fairly be called an author. If you happen to be an essayist, blogger, ghost-writer, etc., then that is likely to be considered a writer much more than the lofty label of author.