Generally, animal products are classed into the categories of meat, dairy, and eggs, and different types of vegetarianism are based on those categories.
"Lacto-ovo vegetarian" is the most common type, and is a person who doesn't eat meat, but can still have dairy and eggs. When someone calls himself just a "vegetarian," he or she usually means this type.
"Lacto vegetarian" means someone who can have dairy but not meat or eggs, and "ovo vegetarian" means someone who can have eggs but not meat or dairy.
"Vegan" means someone who cannot have meat, dairy, or eggs.
Whether it's permissible to use other animal products (e.g. honey) is not specifically covered in the above definitions, but usually lacto-ovo, lacto, and ovo vegetarians are okay with this, while vegans try to avoid all use of animal products, not just in eating but also in clothing, cosmetics, etc..
I hope that's helpful to you!
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