I too have a qualm with the Webster's definition listed above because though I choose not to eat meat I would never contend that it is the "only proper" way to eat.
I think its difficult when one gets caught up in the labeling, because Im sure that you could take a group of twenty people who call themselves "Vegetarian" and they would all have different eating habits and reasons for eating what they do.
I am not obsessive about keeping gelatine or rennet (which I actually hadn't even heard of until I went to England, despite having been vege for 9 years!) out of my diet, but still call myself vegetarian for the sake of ease in communication. Usually I just say "I don't eat meat" if I am able because I just eat what I choose to eat, and don't eat what I don't want to eat. However, sometimes it is easier to ask at a restaurant "Do you have any vegetarian items on the menu?" or is someone asks "Are you vegetarian?" I find it easier to reply "yes" rather than go into a long discussion about the different classifications and kinds of meat products.
While I was vegan for a year I found it impossible to not use any animal products, or use anything that used animal products, (short of going and living self sufficiantly in the woods) as various animal products are used in the processing of gasoline, photocopy toner, and film processing chemicals.