If you eat chicken and fish...you can't call yourself a vegetarian. But you can say you don't eat red meat.
You can call yourself a vegetarian if you eat eggs and dairy...then you are called an ovo-lacto vegetarian. (And of course not eating meat at all) If you don't eat eggs or dairy...you can be called a vegan...and there are varying degrees of that. There are different degrees of vegetarianism then the ones I've mentions...like for example...macrobiotic.