Peafowl is the word that covers the whole kind of bird, male and female together — a peacock is a male peafowl, a peahen is a female one. It is the tidy, technical word, the one you meet in a zoo sign, a bird book, a nature programme, or a wildlife news story. In ordinary conversation people almost never say it; they just say 'peacock' for everything, which is why 'peafowl' can sound slightly bookish when a student uses it in chat. One thing to watch is the plural. Like 'fowl', 'sheep' and 'deer', it usually does not change: one peafowl, ten peafowl. You will sometimes see 'peafowls', especially when someone means several different kinds, and nobody will misunderstand you, but 'peafowl' for both is the safer form. There is also more than one kind — the blue Indian peafowl is the famous one, but green peafowl and the rarer Congo peafowl exist too, which is part of why the general word is useful at all.