What is the medical definition of an addict?

There really isn't 1: because "addict" is not a medical term, and actually our field is coming around to eliminate the words "addict' and "alcoholic" from our vocabularies. The formal term for the disorder is "substance use disorder," where you put the drug involved up front - like "alcohol use disorder" or "opiate use disorder." There are 11 criteria, and if 7 or more present, that is a "severe" disorder= addiction.