Plato was a student of Socrates, Plato knew Socrates and personally wrote about the life of Socrates.
Somebody supposedly wrote something from 399 B.C.E. and you choose to believe it. You have no proof that it’s true, but you still choose to believe that it is. It was allegedly written by Plato and you choose to believe that. You have no proof that it was actually written by Plato, but you still choose to believe that it was.