少林拳 is the title of the martial art (style of Kung Fu) that is taught to the monks and students in the Shaolin Buddhist Monastery.

The addition of Chuan or Quan, which means fist is what signifies that you are talking about this school or form of martial arts.

拳法 is a form of martial arts that can be translated in several ways.

Some will call it “fist principles,” “the way of the fist,” or even “law of the fist.” The first character literally means fist. The second can mean law, method, way, principle, or Buddhist teaching.

Kempo is really a potluck of martial arts. Often a combination of Chinese martial arts such as Shaolin Kung Fu with Japanese martial arts such as Karate, Jujutsu (Jujitsu), Aikido, and others. You may see the term “Kempo Karate,” which basically means Karate with other disciplines added. In this way, Kempo becomes an adjective rather than a title or school of martial arts.

These facts will long be argued by various masters and students of Kempo. Even the argument as to whether it should be spelled “kenpo” or “Kempo” ensues at dojos around the world (the correct Romaji should actually be “kenpou” if you precisely follow the rules).

The benefit of Kempo is that the techniques are easier to learn and master than pure Kung Fu (wu shu). Students are often taught basic Karate moves, kicks, and punches before augmenting the basic skills with complex Kung Fu techniques. This allows students of Kempo to achieve a level where they can defend themselves or fight in a relatively short amount of time (a few years rather than a decade or more).

Because the definition of this word is so fluid, I should make some notes here:

1. Purists in Okinawa will claim that “Okinawa Kenpo” or “Ryukyu Hon Kenpo” is the original and true version of this martial art from the old kingdom. It is actually little or no connection between Okinawa Kenpo and the way the word is used elsewhere.

2. In Chinese, where these characters are pronounced “quan fa” (sometimes Romanized as “chuan fa” because the Chinese-pinyin “q” actually sounds like an English “ch” sound), these characters do not hold the connotation of being a mixed martial art. It is simply defined as “the law of the fist.”

3. My Japanese dictionary oddly defines Kenpo as the “Chinese art of self-defense.” I personally don't feel this is the most common way that people perceive the word but just something you should know.