How does vegetable stock exist?
If I am correct stock is made by leaving the meat bones in water, etc. whereas broth is by using the meat. Then how is there such a thing as vegetable stock if vegetables don't have bones? Wouldn't that mean that vegetable stock = vegetable broth?
stock is made with bones, true by definition.
however, when you're dealing with vegetarian cooking, veg recipes, veg parlance in kitchens, many definitions are expanded to encompass the vegetarian/vegan versions. there is an implied difference in vegetable "broth" and vegetable "stock". veg broth approximates a light chicken broth; veg stock is darker & heavier, either more earthy, root vegetable taste, or typically with mushroom and/or soy (tamari, soy sauce) added to approximate beef broth. since veg broth is a quick, light preparation & veg stock is a more involved & crafted preparation, the broth/stock distinction applies in common parlance, though it may not be technically correct.
I don't know if there are any standardized definitions of what constitutes the lines between broth, bouillon, stock or consommé. Wikipedia has a somewhat helpful article: http://en.wikipedia.org/wiki/Stock_%2...
I'd go along with a general rule of "broth" being something served to you in a cup/bowl while stock is generally referring to an "ingredient".
There are recipes from all over the web for vegetable stock. There are even folks selling highly concentrated vegetable stock as a substitute for demi-glace.