@KNOWITALL When I moved to the midwest I met more people who had no idea of the various definitions than anywhere else I have lived. You live in a part of the country that has lagged behind so to speak on the whole vegetarian thing. I don’t use lag as a negative term, just didn’t have a better word off the top of my head.
Vegan: does not eat any part of any animal, nor milk, things made from milk, nor eggs. Basically anything animal is out. Some vegans don’t even eat honey, but that is an iffy topic.
Vegetarian: is an umbrella term. Vegans are vegetarian, but not all vegetarians are vegan. If someone eats dairy and eggs they can still call themselves vegetarian, but they cannot call themselves vegan.
A vegetarian who eats dairy and eggs is called a lacto ovo vegetarian. Lacto being milk, and ovo being eggs. But, most people just say vegetarian.
You also live in a place where there are quite a few Catholics around probably, and as I said before, Catholics tend to think meat means red meat, or that fish is not meat, so they use the term vegetarian loosely for anyone who does not eat beef or chicken.