What is the distinction of being the king and odeipus rex?examples from the play?
'Rex' is just Latin for 'king.' The two are synonymous.
I'm also fairly certain that this isn't the right subreddit for this question.
Oedipus Rex is Latin for "Oedipus the King". It is an odd translation of the original Greek title of the play, Oidipous Turannos ("Oedipus the Tyrant").