I'm not familiar with the term "electrodiagnostic medicine physician" but that sounds like someone who performs only clinical electrophysiologic studies like EMG/NCS, EEG/EP, intraoperative monitoring, etc. Whereas the latter is a physician who diagnoses and treats patients with neuromuscular problems.
"Electrodiagnostic medicine" is a field that includes a wide range of diagnostic equipment and is not limited to neurology. but includes, for example, cardiology.