Answer:
Vegetarianism, as well as veganism, are defined as diets in which in one way or another, there is either a restriction in the type of animal products that are consumed, or no consumption of these products. However, in veganism, there is even more restriction, as essentially, vegans of different types will eat some types of plant foods, while not others. In vegetarianism, there is absolutely no consumption of animals flesh, but there can be consumption of dairy products and eggs. In veganism, depending on the type, there may be restrictions to some types of meat, or all types, consumption of dairy and eggs, or limitations in these consumptions as well.
As such, the vegetarians are just that, people who do not consume animal flesh of any kind, but can eat dairy and eggs. There are no further groups here
But in Vegans, there are several groups, and their name depends on what they eat, and do not eat. As such we have: Strict Vegan, Lacto-Ovo-Vegan (will eat eggs and dairy), Lacto-Vegan (Only dairy), Fruitarian (only fruits, nuts and certain plants), Flexitarians (sometimes eat meat), Pescatarians (will eat fish), and Raw Foodists (Only fruits, nuts and plants on their raw state)
The types of nutrients that will be lacking, especially for strict vegans and strict vegetarians are: Vitamin B-12, Folic Acid, Calcium, Iron and Zinc. These are all nutrients that must be supplied through supplements on these diets.