The most important difference is this:
In case of persist
method, if the entity that is to be managed in the persistence context, already exists in persistence context, the new one is ignored. (NOTHING happened)
But in case of merge
method, the entity that is already managed in persistence context will be replaced by the new entity (updated) and a copy of this updated entity will return back. (from now on any changes should be made on this returned entity if you want to reflect your changes in persistence context)