Kung fu? In my Karate Kid?

Why is a movie about a young boy learning kung fu called The Karate Kid? For most of the film's young audience, Jaden Smith's break-out movie doesn't explain the confusion. Their parents and older siblings, however, may recall the earlier installments in this series which started with a young Ralph Macchio learning karate from Noriyuki “Pat” Morita, a movie which started as the hero's quest to learn karate to overcome his tormentors and evolved by film's end into a coming-of-age story about the bond between mentor and student. The first Karate Kid struck a chord with audiences, becoming the fifth-highest grossing film of 1984.