Is egg a vagetarian or nonvegeterian food ?

No wonder you are confused. There is no difference between small eggs and large eggs. You either eat eggs you don't. In the past most vegetarian particular from India did not eat eggs since if the egg was fertilized it contained the embryo of a living being. Since mass egg production has evolved, most eggs in the supermarket have never been fertilized because the hens sit in cages and drop the eggs. There is no fertilization there since there are never any roosters near these cages that are kept in large halls and the eggs roll onto a conveyer belt, are washed and are graded into large, medium and small eggs and packaged accordingly. So lately a lot of vegetarians in the West eat eggs, large, medium or small since they contain no life. Vegetarians here eat no flesh from any animal. Vegans eat or drink nothing that comes from an animal, therefore milk and egss are out.

I was under the impression that vegetarians don't eat any meat and that vegans don't eat or use things that come from animals.

vegetarian do eat egg vegans not. but its different.. but if you call yourself a vegetarian and you do eat a egg noone can say "ey, you aren't a vegetarian.." if you are a vegan and eat an egg you can't call yourself a vegan.. the difference is that vegetarian usually dont eat things where animals get hurt (no matter if this is because of get killed or...) they often eat butter, cheese,... vegans don't eat anything which has to do with animals. no butter, no cheese, no meal,... I don't think it's very hard to understand...

All kinds of eggs are non-vegetarian food since it's an animal product.