Either way will add an entity to a PersistenceContext, the difference is in what you do with the entity afterwards.
Persist takes an entity instance, adds it to the context and makes that instance managed (ie future updates to the entity will be tracked)
Merge creates a new instance of your entity, copies the state from the supplied entity, and makes the new copy managed. The instance you pass in will not be managed (any changes you make will not be part of the transaction – unless you call merge again).
MyEntity e = new MyEntity(); // scenario 1 // tran starts em.persist(e); e.setSomeField(someValue); // tran ends, and the row for someField is updated in the database // scenario 2 // tran starts e = new MyEntity(); em.merge(e); e.setSomeField(anotherValue); // tran ends but the row for someField is not updated in the database (you made the changes *after* merging // scenario 3 // tran starts e = new MyEntity(); MyEntity e2 = em.merge(e); e2.setSomeField(anotherValue); // tran ends and the row for someField is updated (the changes were made to e2, not e)