Kiddo's eldest half-sister has become a vegan. Or whatever the proper term is nowadays...
vegan: No meat (yes, seafood is meat), no dairy, no eggs. Strictest category. In its strictest interpretation, anything that's detrimental in any way to animals is off limits. "No leather" types will almost always be vegan. This can go as far as refusing to eat bleached sugar because it's often filtered using bone char. Another item sometimes avoided is gelatin, because it's made from animal collagen (if you see "vegan" labeling on some sort of dietary supplement capsules, it means the capsule material is something else). Sometimes "vegan" also means no honey, on the rationale that bees need it to survive, and they're critical for the plant portion of the food chain (and bees haven't been doing too well in recent years).
vegetarian:
typically shorthand for lacto-ovo-vegetarian, which means everything except meat. However, if in doubt, assume it means vegan. Technically, dairy and egg eating vegetarians are called "lacto-ovo-vegetarians". Obviously, lacto-vegetarianism would be milk and cheese but no eggs or meat, and ovo-vegetarianism would be eggs but no milk, cheese or meat. Some pescetarians (see below) call themselves vegetarian, which IMO is retarded.
pescetarian: no meat except for fish (not sure about other non-fish seafood, I guess they eat that stuff too)... may or may not eat eggs and dairy.
There are lots of people who don't take those labels seriously and will call themselves vegetarian when all they mean is that they won't eat red meat, or as mentioned, pescetarians calling themselves vegetarian. That creates a lot of confusion for food preparers at restaurants, and for people trying to plan private group meals... which leads to things like a vegetarian asking if a dish is vegetarian and getting a "yes" back, then discovering halfway through the meal that it has fish sauce, etc.