Racket and racquet are two spellings of the same word, both with the same definition. Both come from Middle French racquette; the only difference is that the latter is often used in a fancier context and was only popularized because people wanted to make racket look more like the original French. Racquette has an hotly debated origin, but the Oxford English Dictionary lists it as coming from the Arabic word raha, meaning "palm of the hand" (that would be from the Proto-Semitic root r-w-h, "leisure"). By 1785, a new meaning of "fraudulent activity" had emerged for the word racket, quite probably through another definition of "game" that is connected to the other words. Racket meaning "loud noise" is onomatopoeic and unrelated and the word racketeer was coined in 1928.
Hello! I'm Adam Aleksic, a sophomore studying government and linguistics at Harvard University, where I co-founded the Harvard Undergraduate Linguistics Society. In addition to etymology, I also really enjoy politics, vexillology, geography, board games, conlanging, and law.