The Corinthian received the baby already pinioned, and released him
- and obviously knew the significance of the name Oedipus (swollen
foot) - which the Theban Shepherd did not or he would have known when
Oedipus first came to Thebes that he was not only the man he saw kill
Laius, but also the baby he gave away. Surely he would have warned Jocasta
if he knew the young man was Oedipus? So either the Corinthian or King
Polybus must have given him his name. Neither shepherd ever returned
to Cithaeron - both were presumably rewarded for their service to their
respective royal families. The Corinthian became a messenger - and the
Theban was promoted to the king's bodyguard.
So he pretended he had done the service for Jocasta, and hid the truth from her - although he knew perfectly well what the oracle had said (but only the oracle as then known to Jocasta and Laius - that the baby would kill its father. Oedipus does not find out about the mother-marrying addition to the curse until he goes himself to Delphi). Then he was promoted - from shepherd to bodyguard (a big leap in status) - as a reward for his services. Did he feel guilty about this? We know nothing of his feelings on this particular matter - but we know he had feelings - of sympathy for Oedipus at the beginning when he saved him, and at the end when he realised who Oedipus was. But of course both these emotions are bogus - when he saved him he knew he was disobeying the queen and Apollo, and when he finally admitted to knowing him, he knew he was a lifetime too late.
Then he returned to shepherding - a special favour granted by the queen, who respected him for his two services to the family - taking the baby, and loyally bringing back the news of her husband's death. But note that in fact he had lied spectacularly to Jocasta both times. What excuse would he have given her for wanting to leave Thebes?
So what sort of character is he? At first it's tempting to feel rather sorry for him - living with his guilty secrets all those years, and seeming never to betray the family he served so loyally. But the more you think about him, the more wretched he seems - a miserable little man too squeamish to carry out the orders to kill the baby (presumably he got as far as pinioning it, to be left for wild animals or birds to dispose of before he decided to get rid of it otherwise) - and telling the parents a lie; and too frightened to tell what he knew about Laius' death - and lying about it, and prepared to lie, too, about his connection with the Corinthian, until he is finally threatened with physical violence by Oedipus himself.
So the fate of the great man, Oedipus, the seeker after truth, solver of
the Sphinx's riddle, is settled by a common liar - a man who never told
the truth in his life until he was forced to. Oedipus is in no doubt
about his feelings for the fellow - he curses the man who saved his
life, sincerely wishing he had died that day.