Not to be snarky here, but I keep reading references to vegetarians not eating dead animals. Isn't it just animals, period?
Otherwise, they can partake in live goldfish swallowing. 
My understanding of the main difference between a vegetarian and an vegan is that a vegetarian will eat things produced by animals that did not kill the animal, like eggs, milk and honey, while a vegan will not eat anything that has come from an animal.
Yes, but then those are
products made by animals, not the animals themselves, correct (so, not necessary to say "dead animals" when, in fact, being a vegetarian = eating
zero animals)? I'm only being specific here because the thread is discussing the specifics of being vegetarian and being vegetarian vs. being vegan (normally, I wouldn't question that a vegetarian doesn't eat animals, alive or dead, but if the thread is going to split hairs here then it really isn't necessary or appropriate to only specify "dead animals" when meaning ALL animals unless I've really missed something all these years in my understanding of what a vegetarian is). Also, don't vegans tend to have a whole lifestyle attached to being vegan, not just eating habits but no animal products used either (e.g., no leather shoes)?
This discussion reminds me of a season of Survivor when, I believe, one of the contestants stated she's a vegan so she wouldn't eat the cow brain or whatever that was she was supposed to eat. However, she said she could eat a worm (and did) so that always confused me how a worm didn't count as a once-living thing.