PMS is a normal set of physical (and sometimes mild emotional) symptoms that happen in the week before menses onset-- PMS usually doesn't cause much, if any, life disruption. PMDD, on the other hand, is characterized by severe, life-impairing emotional symptoms (and sometimes also physical symptoms) that can last anywhere from 1-2 weeks prior to menses onset.
So there's the severity difference, and there's also the difference that PMDD is primarily characterized first and foremost by emotional symptoms during the 1-2 premenstrual weeks. The core emotional symptoms of PMDD are depression, anxiety, mood swings or rejection sensitivity, and anger/irritability. In order to meet the DSM-5 diagnostic criteria (est 2013) for PMDD, you must have at least 1 of the emotional symptoms (and at least 5 symptoms total) that follow this cyclical pattern of becoming severe premenstrually, and then "shutting off" after menses for an extended period of time (usually during the 1-2 weeks between menses and ovulation).
SO there must be this ON-OFF pattern. Many individuals believe they have PMDD but they actually are experiencing premenstrual exacerbation (PME) of an underlying psychiatric disorder, such as when someone with generalized anxiety disorder has symptoms all the time that are troubling, but develops much more distressing/disabling symptoms in the premenstrual week. We don't know yet whether the underlying biological causes are the same or different from PMDD and PME, but that's something that is being studied.
Updated 22 December, 2018 by Tory Eisenlohr-Moul, PhD