There are 3 main types of vegetarian, these are:

Ovo Lacto Vegetarian.
Don't eat fish or meat but will eat eggs and other dairy products.

Lacto Vegetarian.
Don't eat fish, meat or eggs but will eat milk and other dairy products.

Vegans.
Don't eat fish, meat or any dairy product. Avoid any products of animal origin e.g. don't eat honey. Eat food from plants only.