It’s actually one of those things that varies for each person, how extreme they are with vegetarian. They might avoid anything that contains geletain including gummies or certain medications because it requires an animal byproduct to make.
Eggs and dairy are not part of an animal carcass. You don’t have to kill an animal to enjoy it.
Vegans believe using animals for any food (or maybe even product) is wrong so they avoid eggs, milk, dairy, etc. Or maybe it’s they are vegan in that they only eat eggs or whatever from their own free range chickens. Some vegans won’t get vaccines if they contain egg protein.
Basically often both diets are often moral choices so there can be as much variety to how restrictive or serious it is just like any human will have variety in their morals details even if there is overlap on general idea (ffs just look at Christianity)
And oh there are people who are vegetarian just because they don’t like the taste or texture of meat!
Sorry for the ramble I found this really interesting when I became friends with people who have different diets. It’s interesting how much variety they can have.