"introduction to oedipus the king": what is most likely the author's intent in writing about the difference(s) between sophocles's play and the original myth on which it's based?

The author of the introduction is probably trying to show why Oedipus the Kings is a work of literature worth reading, and what is Sophocles’ merit in writing that play.  

There is a gap of almost twenty centuries between us and Sophocles, so the introduction to the book is trying to show you why its themes are still valuable and worth reading today. It also highlights the difference between the fable of Oedipus and the way Sophocles turns it into a work of art.  

- "about the claims : -

making a claim is just a fancy way of saying that you're stating your main point.' claims are not just opinions. a claim tells what you think is true about a topic based on your knowledge .

about the country claims : -

a counterclaim is just the opposite of a claim. counterclaims are also provable and supportable by reasons and evidence. not just, 'because i said so.' when you're planning an argument, you need to know what the counterclaim might be so that you can make sure that you disprove it with your reasons and evidence your research." - (catherineroberts)