Nope. Vegan is like the "hardcore" version of vegetarian.

Vegetarian:
-No beef
-No pork
-No poultry/fowl
-No meat in general
-SOMETIMES no eggs

Vegan:
-All of the above, plus
-No products made from or by animals; i.e. milk, honey, eggs, yogurt, etc.
-Often also only "naturally" grown veggies and fruits, with no additives or anything like that
-Often no cane sugar (because, apparently, animal fat is used to fertilize cane sugar crops)
-More stuff that I forgot

Basically, what it comes down to is vegetarians don't eat meat, and beyond that, it's up to debate (some eat eggs, some don't, etc.). Vegans don't eat anything that is in any way derived from animals. Also, in my experience, people are generally adopt veganism as a form of protest against animal cruelty and/or the processed, "unnatural" manner in which most food we eat is made. Vegetarians more often tend to be vegetarians simply because they find the idea of eating animals a bit icky. That, or there are specific health reasons. Of course, that's not the rule, but pretty much EVERY vegetarian and vegan I have known falls into categories as such.