Well, attackofthebear got it wrong.
Technically speaking, if you consume dairy or eggs you are still not a true vegetarian. You are a Lacto-ovo Vegetarian. If you just consume dairy (milk & cheese) and not eggs, you are a Lacto Vegetarian. To be a Vegetarian means
NO animal products.
A Vegan takes it a step further and avoids using all animal products in their life--clothing, leather products of any kind, etc. See:
Veganism - Wikipedia, the free encyclopedia.
And yes, unless you KNOW where your dairy or eggs came from, chances are you are contributing to the harm of animals. Regular dairy and regular egg sources are just as shameful and torturous as meat. Free range eggs can be a joke on a label. You have to do your homework.