Right. I don't even think Kung Fu needs to be institutionalized, or in fact can be...I mean, technically, Kung Fu itself is not a martial art. It is a generic name for Chinese Martial Arts in general.
Here is a list of Chinese martial arts from Wikipedia. As you can see, there is a wide variety. Many more than either Korea or Japan.
* Bafaquan (八法拳) - Eight Methods
* Baguazhang (八卦掌; Bagua Zhang) - Eight Trigrams Palm
* Bajiquan (八極拳) - Eight Extremes Fist
* Bak Mei (白眉拳) - White Eyebrow
* Black Tiger Kung Fu (黑虎拳)
* Chaquan (查拳) - Cha Fist
* Changquan (長拳) - Long Fist
* Chuo Jiao (戳腳) - Poking Feet
* Chow Gar - a form of Southern Praying Mantis (南派螳螂)
* Choy Gar (蔡家) - also known as Rat Kung Fu
* Choi Lei Fut (蔡李佛; Càilǐfó)
* Dachengquan (大成拳) - Great Achievement Boxing (Yiquan)
* Ditangquan (地躺拳) - Ground-Prone Fist, Ground Tumbling Boxing
* Do Pi Kung Fu (道派)
* Dragon Kung Fu (Lung Ying) (龍形拳)
* Duan Quan (短拳) - Short Range Boxing
* Emeiquan (峨嵋拳, O Mei Ch'uan)
* Fanziquan (翻子拳) - Overturning Fist, Tumbling Boxing
* Feng Shou - Hand of the Wind
* Five Ancestors (五祖拳) - Wuzuquan or Ngo Cho Kun
* Five Animals (五形)
* Fujian White Crane (白鶴拳)
* Fu Jow Pai (虎爪派) - Tiger Claw System (also titled Black Tiger Kung Fu or Hark Fu Moon)
* Fut Gar - Buddhist Palm
* Gouquan (狗拳) - Dog Fist
* Hong Cha
* Hop Gar (俠家)
* Houquan (猴拳) - Monkey Fist
o Drunken Monkey (醉猴)
* Heihuquan: see Black Tiger Kung Fu (黑虎拳)
* Hsing-i Ch'uan: see Xingyiquan (形意拳)
* Huaquan (華拳) - China Fist
* Hung Fut (洪佛) - Hung and Buddha style kung fu
* Hung Gar (洪家拳; also known as Hung Ga or Hung Kuen) - Shaolin Style and ancestor to many southern styles
* I Liq Chuan (意力拳) - Mind-Body Art, founded by Chin Lik Keong of Malaysia
* Jeet Kune Do (截拳道) - Way of The Intercepting Fist
* Jing Wu Men (精武門) - Jing Wu, a famous school founded in Shanghai that teaches several different styles.
* Jing Quan Do (精拳道) - a modern synthetic style
* Jow-Ga Kung Fu (周家) - Jow family style
* Kuntao - Way of the Fist
* Kuen-Do (拳道) - Way of The Fist
* Lau Gar (刘家) - Lau family style
o Lai-Ga-Sau - A recently created separate branch based in the United Kingdom
* Lai Tung Pai- Shaolin Style that mixes long and short fist
* Lama Pai
* Leopard Kung Fu (豹拳)
* Li (Lee) Family (李家) - Li Family or Lee Family style
* Liu Seong Kuntao (also Liu Seong Gung Fu, Liu Seong Chuan Fa) - A Chinese art with Indonesian influence, practiced primarily in the United States
* Liuhebafa Chuan (六合八法; Liu He Pa Fa, Lok Hup Ba Fa) - Six Harmonies, Eight Methods or Water Boxing
* Luohan Quan (羅漢拳) Arhat Boxing, Law Horn Kuen
* Mei Hua Quan (梅花拳 Plum Blossom Fist)
* Mian Quan (棉花拳擊 Cotton Boxing)
* Mizongyi (迷蹤羅漢拳; Mízōngquán) - Lost Track Fist (also known as My Jong Law Horn)
* Mok Gar (莫家拳) Mok family style
* Monkey Kung Fu see Houquan
* Nam Pai Chuan (南派拳)
* Nan Quan (南拳) - Southern Fist
* Northern Praying Mantis (北派螳螂拳)
* Northern Shaolin (北少林) - Bak Sil Lum
* Pai lum (白龍) - White Dragon, Pai Family Method, a modern style based on Kenpo with Chinese influences found mainly in the US and Canada
* Paochui (炮捶) - Cannon Fist, Sanhaung Paochui
* Piguaquan (劈掛拳) - Chop-Hitch Fist, Axe-hitch boxing
* Praying Mantis: see either Northern or Southern Praying Mantis
* Sanda (散打) or Sanshou (散手) - Free Fighting
* San Soo (散手)
* Shaolin Nam Pai Chuan (少林南派拳) - Southern Shaolin Boxing
* Shaolin Quan (少林拳)
* Shen Lung Kung Fu (神龍功夫) - Modern variations of Southern style Chinese martial arts based in the United States
* Shequan (蛇拳) - Snake Fist
* Shuai Chiao (摔跤; Shuaijiao) - Chinese Wrestling
* Southern Praying Mantis (南派螳螂拳)
* Tai Chi Chuan (太極拳 Tai Chi Chuan, Taijiquan) - Supreme Ultimate Boxing
o Chen style tai chi chuan
o Yang style tai chi chuan
o Wu/Hao style tai chi chuan
o Wu style tai chi chuan
o Sun style tai chi chuan
* Tantui (彈腿/譚腿) - Spring Leg style
* Tibetan White Crane (白鶴派)
* T'ien Shan Pai (天山派)
* Tongbeiquan (通背拳) - Through-the-Back Fist
* White Crane: see either Fujian White Crane or Tibetan White Crane
* Wing Chun (詠春 or 永春) - See also Wing Tsun
* Wudangquan (武當拳)
* Wu Wei Gung Fu (無為功夫)- "The Spontaneous Movement of the Gung Fu". A modern composite style containing elements of Jeet Kune Do, Wing Chun and other martial arts
* Xingyiquan (形意拳; Hsing-i Chuan) - Form-Intent Fist
* Yau Kung Mun (软功門) - Flexible-Power Style
* Yingzhaoquan (鷹爪拳) - Eagle Claw Fist
* Yuejiaquan (岳家槍) - Yue family Fist/Boxing
* Yiquan (意拳; I Ch'uan) - Mind Boxing
* Zhuan Shu Kuan - A modern composite style containing elements of Tae Kwon Do, Muay Thai and Changquan. It is based in the United Kingdom
* Zi Ran Men (自然门) - Natural Boxing or "fist of nature"
* Zui Quan (醉拳) - Drunken Fist