Most vegetarians do NOT eat animals.
There are many types of vegetarians. Vegetarian is merely a way of describing one's diet. All vegetarians eat vegetables, fruit, and grains. Below is a list of what certain types of vegetarians eat on top of this.
Vegans: just consume vegetables, fruit, and grains and grain products that do not include eggs, gelatin, or other animal by-products.
Ovo-Vegetarians: Also eat eggs.
Lacto-Vegetarians: Also consume milk and milk products (milk, cheese, cream, yogurt, ...)
Lacto-Ovo-Vegetarians: Also eat both eggs and milk products.
Pollo-Vegetarians: Also eat poultry (and usually eggs)
Pesco-Vegetarians: Also eat fish
Quasi-Vegetarian: Eats vegetarian meals occasionally.