Shaolin Kung Fu refers to a collection of Chinese martial arts that claim affiliation with the Shaolin Monastery.
Of the multitude styles of kung fu and wushu, only some are actually related to Shaolin. After the loss of records during the 20th Century Cultural Revolution it would be almost impossible for a particular style to conclusively establish a connection to the Temple, aside from a few very well known systems, such as Xiao Hong Quan, the Da Hong Quan, Yin Shou Gun, Damo Sword, etc.
Read more about Shaolin Kung Fu: Internal and External Arts, Tang Dynasty (618–907), Ming Dynasty (1368–1644), Influence Outside China, In Popular Culture, List of Styles Currently Taught At The Temple, Special Shaolin Training Methods, Contemporary Training At The Shaolin Temple