Veganism is a philosophy and 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; and by extension, promotes the development and use of animal-free alternatives for the benefit of animals, humans and the environment. In dietary terms it denotes the practice of dispensing with all products derived wholly or partly from animals.
It sounds like you think the only options are veganism (which you call vegetarianism) or carnism
Vegetarianism is a diet, veganism is a philosophy. Lacto-ovo-vegetarianism is a self-soothing delusion.
No, they both describe diets. One refrains from eating meat, the other refrains from eating all animal products
https://www.vegansociety.com/go-vegan/definition-veganism