A vegan is the next step after vegetarian. I'll put it in steps so you can see what I'm talking about, as the difference between vegetarians is new to me, it may be unheard of for you, but whatever.
Lacto-Evo Vegetarians vegetarian that most people think of. They don't eat meat, but they eat milk and eggs, and anything derived from the two. They also eat other animal byproducts such as honey.
Lacto Vegetarian: Same as a lacto-evo vegetarian, except Lacto's don't eat anything with eggs or that was derived from eggs.
Evo Vegetarian: Same as a lacto-evo vegetarian, except Evo's don't eat anything with milk or that was derived from milk.
And finally, to answer your question:
Vegan:Doesn't eat meat or any meat products such as milk, eggs, honey, or some of the lesser known ones like Gelatin (found in most Gelatinous substances of the American food industry, like jello and fruit snacks, gelatin is made from pig's hoof and pig's bones)
I'm a Lacto-Evo Vegetarian.