The difference between the reality of Oedipus’s actions versus the appearance is central to the story. In it, Oedipus does many things that seem to be relatively straightforward, when in reality, they are twisted and all correlated to the prophecy of the Oracle.
For instance, when Oedipus kills the man on the road, it seems like a standard case of road rage and an argument gone bad. However, we later (much later) learn that this man was his father and that he had killed the King, as stated in the prophecy.
After that, he goes on to marry the Queen, as he has saved the city from the Sphinx. This appears straightforward but in reality is another aspect of the Prophecy—he has married his mother.
Finally, when he declares that the killer of the king must be found and executed, Tiresias warns him about this action, foreshadowing the revelation that it’s not as it seems. It is soon revealed that this action is essentially putting a target on his own head, as he killed the king.