From Wikipedia

Shaolin - Masters Of Kung Fu

Shaolin Kung Fu refers to a collection of Chinese martial arts that claim affiliation with the Shaolin Monastery. Of the tens of thousands of kung fu wushu styles, several hundred might have some relationship to Shaolin; however, aside from a few very well known systems, such as Xiao Hong Quan, the Da Hong Quan, Yin Shou Gun, Damo Sword, etc., it would be almost impossible to establish a verifiable connection to the Temple for any one particular art.

Huang Zongxi described Chinese martial arts in terms of Shaolin or external arts versus Wudang or internal arts in 1669.  It has been since then that Shaolin has been popularly synonymous for what are considered the external Chinese martial arts, regardless of whether or not the particular style in question has any connection to the Shaolin Monastery. Some say that there is no differentiation between the so-called internal and external systems of the Chinese martial arts, while other well known teachers have expressed differing opinions. For example, the Taijiquan teacher Wu Jianquan:

Those who practice Shaolinquan leap about with strength and force; people not proficient at this kind of training soon lose their breath and are exhausted. Taijiquan is unlike this. Strive for quiescence of body, mind and intention.

In 1784 the Boxing Classic: Essential Boxing Methods made the earliest extant reference to the Shaolin Monastery as Chinese boxing's place of origin. Again, this is a misconception, as Chinese martial arts pre-date the construction of the Shaolin Temple by at least several hundred years.