The correct word is 'cheat'. 'cheater' is poor English (although possibly more acceptable in American English) A liar is someone who deliberately says things that are incorrect. A cheat is someone who either says something, or does something, usually to gain some unfair benefit. So - if you copied someone's test, you are a cheat. If you hide an extra card in your hand, you are a cheat. If you tell me I am good looking, you are a liar ;) You can of course cheat, by telling lies.

"To lie" means "to say something untrue, in order to deceive somebody else." "To cheat" means to "to do something unethical, and usually sneaky, in order to get an unfair advantage." I was playing Scrabble with my 8-year-old grandson. It was his turn. While I was out of the room, he made two moves instead of one. He cheated. When I asked him "Did you take two turns instead of one?" he looked embarrassed and said "Yes." So, he cheated, but he did not lie about it. If I say--out of vanity--that "I am six feet tall" when I am really one inch shorter, and I expect you to believe me, then I am lying, but I am not cheating. Often, the reason for telling a lie is to cheat someone. Often, "cheating" involves money. A special use of "to cheat" is "to be sexually unfaithful." Thus, in the United States anyway, we might read that "Ben Affleck was caught cheating on Jennifer Garner with Christine Ouzounian." Here, "cheating" means "cheating on his marriage vow." I didn't know that the specific form "cheater" was U.S.-only, but Gary is correct. OxfordDictionaries.com calls it "North American." ahdictionaries.com (my favorite U.S. dictionary) simply lists it, without comment. (It is rare and out-of-date, but "cheaters" can mean "eyeglasses." I'm not sure I've ever heard anybody use it, except in a 1938 song, "Jeepers, Creepers.")