Thanks for these questions. Initially it wasn't clear to me what the difference was either, but now I understand the distinction a little more.
The ORMs discussed in the article map a whole object model to a whole relational model. The idea is that a single piece of primitive data, say a bool flag on an entity, will have one location in the relational model, and one location in the object model, and the mapper's job is to get the data from one to the other and back again.
Hibernate will guarantee things about the object model, for example within a particular session, the entity A which maps to a record with id 1 in the database will be represented by the same object instance, so even if A is referenced indirectly through two different routes, eg, obj.foo.a and obj.bar.a, it would reference the same instance of A. The instance will only be fetched once, can be mutated through either route, and then saved back to the database using the mapping.
That's the sort of thing which is possible with a single mapping, but the abstraction breaks down outside that mapping. For example, questions like this on StackOverflow:
http://stackoverflow.com/questions/2470129/how-can-one-fetch...
He wants to select part of a database record, not the whole record. The mapping will only be defined for whole entities, so he has to use the complex projection syntax instead of a normal fetch. The top answer suggests mapping the data into a User object anyway, which will result in his code having some User objects will all their properties set, and some with just a subset.
This puts pressure on the programmer to stick to the single mapping. Partial fetches like this could lead to an object which represents a particular user which may or may not still be the same instance, and it may or may not support being saved back into the database.
> Are you not in full control of them?
So, yes, you are in full control, but the benefits come when there is a single mapping between the relational model and the object model. In practice, there isn't a single object model, let alone a single mapping.