what makes it a Drahthaar rather than a Wirehair?
Drahthaar does mean wire hair. What sets it apart is the breed club and the standards it is breed in. Instead of the breed club being here in America, it is in Germany. They (the German breed club) Make sure that all breeding are done to the standards set forth by the club are followed. The first time these dogs are inspected is at 8 weeks when each is given a ear tattoo for identification. Then as I said above, each dog owner who has ambitions of breeding their dog must test their dog in multiple required hunt and conformation tests where the dog is evaluated on multiple aspects not just their upland abilities.
And yes compared to the AKC hunt tests/field trials that you participate in the dogs interact much less with the handler. This does not mean that the dog has minimal training, it's training is just a little different. I will still FF my dog and teach him to handle, I just won't worry if he does not follow the exact line I send him on.