White Crane Kung Fu is a powerful and old Chinese Martial Art. It is said to have been developed by a daughter of the Fang family in Fujian province, but this may not be true. Track the lineage back a little further and there seems to be a definite link to Bak Mei.
To understand this old kung fu style, one should probably analyze such karate kata as Sanchin and Hakutsuru. Sanchin kata, in particular, is present in many Karate schools, but the earliest, and least diluted version can be found in Uechi Ryu Karate. Examining the form in that system and one will see the dependence on the hourglass stance and a similarity of hand motion.
The problem with the Japanese variations, in this author's opinion, is that the forms are taught either for dynamic tension (muscle building), breathing, or just technique. If one studies the earlier versions of the White Crane Forms, one will see the movements rendered more for the creation of Chi. The movements are more gentle, yet the stance is deeply rooted, and the mind is thus allowed to instill imagination and will into the movements.
Go back even earlier, to the Bak Mei variation of white crane kung fu, and one will see an explosiveness that is designed for intense combat. The fists don't come back to the body between 'launches,' and the entire body lurches into each movement. The result is a quickness and ferocity that outdoes karate variations of the forms.
The history of this form, as indicated, can be confusing. There is the karate version, and this is connected to China predominately through Uechi Ryu and the studies of Kanbun Uechi. He is said to have spent some thirteen years learning three specific kung fu forms, all of which, should one eliminate the focus on dynamic tension, have similarity to Chinese White Crane Kung Fu.
In China, the legend is that this unique kung fu was created by a daughter of the Fang family. She is said to have studied kung fu with her father, and then to have been inspired by the self defense movements of a white crane that fended off a stick she thrust at it. While there does seem to be a connection, it seems more like a teaching legend, and the truth is probably a lineage, rather than an inspiration.
The strongest possibility is that these forms were originated in the Bak Mei Kung Fu school. Bak Mei is strong in the Fujian (Fukien) province of China, and the martial art could easily have been passed to the Fang family. This allows for the possibility of the Karate connection, also.
In closing, if one inspects the structure and moves of the form, paying attention to Uechi Karate versions of Sanchin and the Bak Mei versions of the form Jik Bo, one can see a definite relationship. In truth, the author recommends seeking out all versions of the form, and distilling them for focus on dynamic tension, breathing, technique, explosiveness, or whatever you wish to explore. Such forms as Sanchin, Hakutsuru, and the like are very pure in their white crane kung fu lineage, and quite possibly the missing link to Karate.