An electronic medical record is typically a record that is at a provider's location. Given that we all go to see our GPs, we want to build electronic medical records whereby a vast majority of your records will be there. Having said that, as individuals we seek services at times in emergency rooms, at clinics, in private labs, etc. At times, those records are locked away and don't actually make it back to the GP.
An electronic health record is ubiquitous around the patient. No matter where the patient moves, all of their records, all of their medication histories, lab results, and diagnostic imaging will be available. If the GP can download other points of care where care has been given into their medical record, it really becomes an electronic health record.
So one is ubiquitous around the patient—the health record—and the other is more location-specific.