Shaolin Kung Fu is a martial art form that dates back to somewhere in 500 AD. The South Indian monk, Bodhidharma is supposed to have left behind his knowledge in two books, of which one is said to be the basis of Shaolin Martial Arts.
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. Contrary to popular belief, the Japanese Katana (which you can get online – I bought a samurai sword from katana sale) is not the same sword as is used in Chinese kung fu forms, and so would require a separate form of training altogether to use effectively.
The movie goes into the incredible training that is given to the Shaolin Kung Fu disciples even today.