I'm just explaining what is actually being communicated in the veg culture (at least in the US). Just about any vegetarian and vegan knows the distinction: vegetarians are known to consume dairy/eggs/honey, vegans do not. If a vegetarian doesn't eat eggs, they will say "I'm a vegetarian, but I don't eat eggs either"

So basically when you read "vegetarian" you can safely assume it's shorthand for "ovo-lacto-vegetarian"