I thought that when people make themselves vomit in order to lose weight, they have bulimia nervosa and not anorexia. Is this correct?

Actually, this is a common misconception. Let me help clarify the distinction between anorexia and bulimia, as they are currently defined within the DSM-IV-TR.

The behaviors associated with anorexia and bulimia is often similar; the distinguishing factor between the two illnesses is the extent of weight loss in a patient. The diagnosis of anorexia only applies to an underweight patient. For example, a person engaging in binge eating or purging who weighs less than 85% of their expected normal weight would meet the diagnostic criteria for anorexia nervosa, while a normal-weight person who engages in similar behavior would be diagnosed with bulimia nervosa.

As many as 40–60% of people who seek treatment for anorexia may engage in binge/purge behavior, so while these behaviors are commonly thought to be exclusive to bulimia, they are actually fairly common in anorexia as well (Hsu 1988). In fact, a person may be diagnosed with anorexia nervosa when he or she is severely underweight but receive a diagnosis of bulimia nervosa if the symptoms persist after weight-gain. Research has shown that approximately 20–50% of patients diagnosed with anorexia will at some time be diagnosed with bulimia nervosa, while nearly 25–30% of those with bulimia nervosa have a history of anorexia. Again, the key distinguishing factor is how much weight loss has occurred.

As many as 40–60% of people who seek treatment for anorexia may engage in binge/purge behavior.