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This all depends on the ability of the writer and they way they think and write.
A screenplay is usually written in a way that has clear visual information, however without too much description and direction, so as to leave it open to interpretation for the director. A screenplay will go through several hands and edits before making it to screen. We cannot specify too much information on the emotions or inside dialogue of a character, unless it is vital to the story, or it is a specific style of the actual movie. We do this because we have to also leave some ambiguity for the actors, so they can also make the characters their own. A screenplay also follows a much more specific structure. (There is more info, but I think it might turn into an essay)
Novels or short stories however are quite different. In a book you have the freedom to go into in-depth descriptions, get into the heads of the characters and you have more freedom in structure and imagery; it is solely up to you to create the world that the readers will experience.
Basically it all depends on the story, writer, ability and mentality. You can just as easily write in both styles, but prepared to shift your method of thinking and approach for each.
This depends on the writer. Some writers are adept in both fields; while others are more comfortable with either one of these areas.
These two are diverse skills and you may not find every writer expert in both. Therefore to write for reader is easy for book writer and play writing is easy for play writer.