You can purge and still be anorexic, purging comes in different forms - such as throwing up, taking laxatives, enemas, and whatnot. It's actually as the previous post stated, binge-purge subtypes which are quite common.
The main difference between someone who is anorexic and someone who is bulimic is actually down their habits. Anorexic people want to disappear, look dangerously thin and sometimes can relish on being the skinniest person, or attracting concerned attention from others about their weight. They don't actually know how serious is can be, but it's something they don't want to lose control of, they want to be the skinniest person, they want to be skinnier than a model - the skinniest person you'll see in your life. It means they've done well in their eyes (SOMETIMES) but it is all about obsessive restriction in a general sense, and more restricted diets are praised in the pro-ana community.
A bulimic, slightly different, they do weight management, they want to be healthy or underweight - yes, but not dangerously thin. Most bulimics are actually normal weight or overweight. There isn't a need to be incredibly skinny, unlike anorexic people, Bulimics tend to be less focused on willpower (the power of control to not eat, which a lot of people with anorexia practice - hence it taking over their entire lives) but weight management. Bulimics suffer from serious relationships with food, as it's something they really can't control properly - which is why they have a vicious cycle of binging and purging. It's usually associated with overeating and then purging/exercising. Anorexia is revolved around undereating - then purging or exercising.
TLDR: Anorexic people can purge if it makes them feel skinnier.