What is an author for the following two critics: Facoult and Barthes? What are the differences and connections?

Let me start, of course, but recommending that you read
the two short essays by the critics you name, Barthes' "The Death of the Author" and
Foucault's "What is an Author?". But you want answers, of course, and not simply
recommendations, so I'll write a little more!

The link
provided below gives a pretty substantial discussion of these two works and some points
of simiilarity and difference.

For me, the greatest
similiarity is that both critics are challenging the dominant concept of the "author."
Even today, after decades of such challenges, many people continue to believe that the
author is everything -- e.g. the author is in complete control of the text, the reader
must know something about the author in order to understand the text, the "author's
purpose" (a recurring item on standardized tests in schools in the United States) is
something that deserves our full attention, and so
on.

Again, for me, the greatest difference is what the two
critics emphasize in their pieces. Barthes wishes to shift everything from the author to
the text and the reader, whereas Foucault wishes to explore the various historical
"functions" of the author. This difference, to me, says everything about the differences
between these two critics. Barthes (in his poststructuralist years, at least) is all
about the "pleasure of the text," for example, and Foucault is all about how
knowledge and experience are organized (e.g. his famous study The History of
Sexuality).