in pure literary analysis (for those who don't know, i teach literature in uni and am working on my PhD right now), they are not quite the same person !
Jane Austen as a writer is a woman who writes books and lived in the XIXth century, was born in Steventon on December 16th 1775, etc.
Jane Austen as an author is the "idea of a person", regardless of her biography, who has written Sense and Sensibility and Pride and prejudice
is that clear? in a text, we look for the 'author' of the book, but we can also get interested in the 'writer' Jane Austen on a pure history of ltierature aspect