The baby boy becomes an old man. They are different. By giving this "person" a name eg. John there is an illusion of an entity. By convention John was born on such a date, he grew old and died on such a date. In reality John the old man was never born, only the baby John. John the baby never died, only the old man John. In terms of ultimate truth no one was born and no one died. Everything is becoming. This is a universal process, a constant flux. It is when we miss the continuity of action that we speak in terms of things (atta/self) rather than processes or becomings. Upadana pacaya bhavo [Existence is dependent on clinging to a self/being].