Ours can get sent to the pharmacy electronically, or printed off the doc's computer and handed to us. Some have to go to a specified pharmacy because of insurance; others not.
Errors can creep up either way. Electronic prescriptions are a bit of a sore spot. There's little way for a patient to spot an error and have the doctor fix it until it's being picked up. For those that go a long way and are filled mail order, this can be a major hassle. The battles with ins. company and their specified pharmacy never cease; incompetence abounds. YMMV (at least I hope it does!)
Doc