@Stepstepmother
Your example is completely irrelevant, it's not comparable in the slightest. Vegetarianism is not the same as veganism.
The Vegan Society (whose founders coined the term vegan, so if anyone gets to define it, they do) say: "Veganism is a way of living which seeks to exclude, as far as is possible and practicable, all forms of exploitation of, and cruelty to, animals for food, clothing or any other purpose."
It's very clearly a) not just a diet, but an entire philosophy/lifestyle, and b) motivated by caring about animal rights. Not the environment. Not health.
On the other hand, the Vegetarian Society defines a vegetarian as follows:
"A vegetarian is someone who lives on a diet of grains, pulses, legumes, nuts, seeds, vegetables, fruits, fungi, algae, yeast and/or some other non-animal-based foods (e.g. salt) with, or without, dairy products, honey and/or eggs. A vegetarian does not eat foods that consist of, or have been produced with the aid of products consisting of or created from, any part of the body of a living or dead animal. This includes meat, poultry, fish, shellfish, insects, by-products of slaughter* or any food made with processing aids created from these."
It's solely a diet by that definition. Doesn't mention anything about motivation. Plenty of people who eat vegetarian wear leather (I used to, though now think I was a hypocrite). So yes, if some Hindus don't eat meat, they are vegetarian, regardless of how they feel about animals.
But you are not vegan, and never will be till you care about non-human animals.