The aim of this study was to identify characteristics that differentiate patients who complete suicide (SC) from patients with suicide attempts (SA) while undergoing treatment in Norway. We examined data from the Norwegian System of Patient Injury Compensation (Norsk Pasientskade Erstatning—NPE). Data were extracted from NPE case records from a 10-year period (2009–2019) for 356 individuals who attempted (n = 78) or died by (n = 278) suicide. The two groups differed significantly in the types of medical errors identified by experts. Inadequate suicide risk assessment tended to be proportionally and significantly more prevalent among SC compared to SA. There was a weak but significant trend that SA had received medication only, whereas SC had received both medication and psychotherapy. There were no significant differences with respect to age group, gender, diagnostic category, number of previous suicide attempts, inpatient/outpatient status, or category of responsible clinic. We conclude that suicide attempters and suicide completers differed in terms of identified medical errors. Focusing on the prevention of these and other types of errors could help to reduce the number of suicides of patients in treatment.