Don't laugh, I've had large anemones eat fairly large fish. The various species of hawks seem prone to this, because they like to perch on rocks. If they perch on an anemone, it's all over, and the anemone just had a very expensive dinner.
That is correct, carpet anemones have much more powerful stinging cells. They are one of the few that can really do a number on you, if you get stung in an area where your skin is thin, like the underside of your wrists, or a small cut.