Varför heter titeln "Karate Kid" när de använder Kung fu?

Eftersom det är ett återskapande av en film med samma namn och de ville inte förlora på populariteten av den äldre filmen. Om du har sett båda filmerna märker du att båda berättelserna är ganska lika, bara ersätter Karate med Kung-fu och ändrar platsen.

Sony tänkte på ett tillfälle om att ändra det men de gjorde inte i slutändan:

Despite maintaining the original title, the 2010 remake does not feature karate, which is from Okinawa, but focuses on the main character learning kung fu in China. Chan told interviewers that film cast members generally referred to the film as The Kung Fu Kid, and he believed the film would only be called The Karate Kid in America, and The Kung Fu Kid in China.

Sony had considered changing title of the film, but Jerry Weintraub, one of the producers, rejected the idea. Weintraub was also the producer of the original Karate Kid. - Wikipedia

2010-filmen Karate Kid är en remake av en 1984-film med samma namn. I den filmen lär Daniel sig Karate och deltar i en turnering .

Härifrån :

Miyagi proposes that Daniel will enter the Under-18 All-Valley Karate Tournament, where he can compete with all the Cobra Kai students, and he requests that the bullying should cease while Daniel trains. Kreese agrees to the terms, and warns that if Daniel does not appear at the tournament, the harassment will resume on Daniel and Miyagi.

Miyagi begins Daniel's training by telling him that Daniel is required to commit unequivocally to Miyagi's curriculum, and to obey Miyagi's every instruction, without question. After Daniel agrees, Miyagi assigns Daniel to complete various lengthy, menial chores that appear to have nothing to do with karate.