According to the Vegetarian Society there are 3 different types of vegetarians:
Ovo-lacto vegetarians eat animal products such as milk, cheese and eggs, but nothing that has been produced as a results of an animal being slaughtered such as meat, fish or poultry.
Lacto vegetarians eat animal products such as milk or cheese, but will not eat eggs or products that have been produced as a results of the animal being slaughtered.
Vegans or strict vegetarians avoid all animal products, including honey and only eat food from plant sources.