(2 and 3) I read labels before I make any assumptions: I assume that a product labeled vegetarian might contain milk, eggs, honey, or any number of additives which are not vegan.
I really appreciate it when I see a product labeled vegan and feel motivated to buy it. Even though I am lacto-ovo, I really do appreciate it when companies decide to make their products 100% animal-free.
By the way, I also assume that Vegan means no testing on animals, no animal products used during processing -- ie., juices clarified with gelatin.
Another interesting note: If it's not labeled vegan, maybe there's an animal product in there that I am not familiar with yet. On a more curious day, I might research any unknown ingredients on the web.