Vegetarians eat chicken and fish. A vegetarian eats no flesh, fowl or fish.
Total vegetarians exclude eggs and diary products as well.
Getting enough protein is a problem for vegetarians. It's nearly impossible to design a diet with a variety of whole foods that is deficient in protein. If you consume enough calories to meet your energy needs, you'll get more than enough protein. If a little protein is good, a lot is better. In developed countries, too much protein is a much bigger health threat than too little.