Yes. They are suitable for vegetarians (ovo-lacto) like me, but not for vegans who do not eat any animal products (including honey, or sugar processed with bone char).
Vegans, and some vegetarians (such as myself) also avoid fur and leather products such as shoes and belts and purses made from animal hydes.
@Jleslie is correct. Vegetarians and vegans do not eat fish either, in addition to meat, and fowl (which are all considered to be the same thing—dead animals).
People who claim to be vegetarians, that also eat fish, can be called “peacatarians”, but they are not vegetarians. They are just people who don’t eat red meat, for whatever reason.
If you are hosting a “vegetarian” or attempting to find a suitable place to dine with a “vegetarian” it’s easier to ask that person what they can and can’t eat.