Are PhD students enrolled or hired?
At least in Germany, doctoral candidates are either employed as Wissenschaftliche Mitarbeiter (research assistants) or given stipends as "doctoral fellows."

However, regardless of how they are paid for their efforts, they must "enroll" as doctoral candidates with one of the faculties if they are to receive a degree. So, to a certain extent, they are treated like students as well, and have many of the same privileges (for instance, they are entitled to the same student benefits when they register).

So, to a certain extent, they are both; however, their employment contract, rather than student regulations, tends to be the "controlling factor" in their treatment.