I don't see why the definition should change based on whether someone is a vegetarian for ethical reasons or health reasons or environmental reasons or any other reason. I have always gone by the definitions of vegetarian and vegan from The Vegetarian Resource Group's
FAQs page:
What are the different types of vegetarians?
1) Lacto-Ovo Vegetarian: does not eat meat, fish or fowl. Eats dairy and egg products.
2) Ovo Vegetarian: does not eat meat, fish, fowl or dairy products. Eats egg products.
3) Lacto Vegetarian: does not eat meat, fish, fowl or eggs. Eats dairy products.
4) Vegan: does not eat any animal products including meat, fish, fowl, eggs, dairy, honey, etc. Most vegans do not use any animal products such as silk, leather, wool, etc. as well.
Having said that, I do find a lot of restaurant servers are still confused over the meaning of the word vegetarian. Many times when I say "I'm a vegetarian" I am asked "Do you eat fish?"