As a vegetarian of over 20 years, let me explain:
For a pizza to be vegetarian it can contain no meat, no fish, no poultry, no seafood and no non-vegetarian cheese.
Many cheeses are not suitable for vegetarians as they are made with animal rennet (the stomach lining of slaughtered calves).
True parmesan cheese (parmigiano) is never suitable for vegetarians.
At most pizza restaurants, the pizzas are listed by name and the name usually includes some mention of the ingredients:
Meat Feast
Stuffed Crust Three Cheese
Pizza al Funghi (Mushroom)
Spinach and Ricotta pizza
etc etc
It is just possible that if there were only one pizza on the menu which was suitable for vegetarians, the restaurant might choose to simply call it "Vegetarian Pizza" but it's very unlikely.
There is no such thing as a standard Vegetarian Pizza - there are dozens of combinations of toppings which could be put on a pizza and it would still be vegetarian. Normally, the pizzas which are suitable for vegetarians are marked with a "V" on the menu.