There is a difference between vegetarians and vegans. Vegans are stricter than vegetarians in regards to the foods and drinks that they consume. Vegans will not consume animals or animal by-products. Vegetarians, on the other hand, may eat the by-products like cheese or milk.
These products are made by the animals. However, it all depends upon the vegetarian and vegan. Some vegans and vegetarians are stricter than others. Therefore, for the most part, vegetarians would eat goat cheese because they will eat the by-products compared to vegans who would not.
Vegetarians would also eat eggs and milk from both cows and goats. They would also consume by-products from other animals as well. However, they would not eat the meat from the cows and goats because you would have to kill it.