As we use these terms, we mean:

omnivore = eats animals
(meat, poultry, fish),
gelatin, rennet cheese,
dairy, eggs, honey,
grains, beans, vegetables, fruit

vegetarian = eats
dairy, eggs, honey,
grains, beans, vegetables, fruit

vegan = eats
grains, beans, vegetables, fruit

There are many other eating lifestyles, but these are the most widespread.