Usual custom dictates that the author of a book is the one who owns it and the director of a movie is the one who owns and the choreographer of a dance is the one who *owns** it
Lucas' Indiana Jones
Camus' The Stranger
Balanchine's The Nutcraker
in the above, different versions would be referred to by the owners name
Teacher: So class,what did you think of The Stranger?
Student: Which one?
Orson Welles' The Stranger
Guillermo Amoedo's The Stranger
Robert Leiberman's The Stranger
are all different films with the same title.
Which Nutcracker are they doing this year?
Balanchine's The Nutcracker
Petipa's The Nutcracker
San Francisco Ballet's The Nutcracker
Ballet Scotland's The Nutcracker
are different versions of the same dance.
To say that something is by someone might lead to some ambiguity of what's being referred to since movies can be based on a story in a book
P1: In Cold Blood is by Richard Brooks
P2: No its not, it's by Truman Capote
P1: I was talking about the movie
P2: But the book is much better
In Cold Blood directed by Richard Brooks based on a story by Truman Capote
has no ambiguity.
In movies there is the added layer of a screenwriter who's name might be used if they happen to be famous.
Among the two options you suggested, 'second best' is what I would go for. Just 'second' could imply anything. The first thing that comes to mind with just 'second' is that the student was the second student to join a class.
Best Answer
Your question centers around
So to describe an author's book
are both correct.
"Best-seller book" would not be correct, however
is correct.