There's an article titled Vegetarians Who Eat Fish Are Actually Onto Something which says,
I’m out besmirching Malibu’s pristine sands to decide if pescetarianism—a vegetarian diet supplemented only by fish—has more to it than guilt-free sushi. We’ve all met the vegetarian who casually mentions that he or she eats fish. Logic aside, it’s a fairly common mindset with arguments based on ethics, environmentalism, and health.
Is it true to say that in American English (where the referenced article was written), the word "vegetarian" is often used to identify people or diets which do include eating fish?