Tai Chi Chuan Dao in Chinese / Japanese...

太極拳道 is the common Tai Chi Chuan title with “Dao” (the Way) added to the end.

If you're not sure, I suggest shorter titles such as “Tai Chi Chuan,” or just “Tai Chi.”

This can be a Mandarin Chinese surname that romanizes as Chuan.

The actual meaning of the character is armlet or bracelet.

少林長拳 is a combination of two titles. The first two characters mean little forest, as in the little forest of the Shaolin monks (shao lin = little forest). The second two characters mean “long fist.”

This title is specific to a particular technique - if you are studying Shaolin Chang Chuan, then you are already aware of all the ramifications.

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.

Peng, Lu, Ji, An, Cai, Lie, Zhou, and Kao are the eight fundamentals or forces of Tai Chi Chuan or Taiqiquan.

棚 (Peng) refers to the outward (or upward) expansion of energy.
履 (Lu) is often referred to as “rollback.” Lu is the ability to absorb, yield/deflect incoming force.
擠 (Ji) is often thought of as a “forward press.” However, it is also best described as a “squeezing out of space.”
按 (An) is a downward movement of energy, best translated as “(relaxed) sinking.”
採 (Cai or Tsai) translated as “downward pluck.” Cai is a combination of Lu and An.
列 (Lie or Lieh) is “Split” and is a combination of Peng and Ji.
肘 (Zhou) Elbowing.
靠 (Kao) Shouldering (for when the arms are bound/distance is too close to punch).

Source: https://combativecorner.wordpress.com/2015/12/03/the-8-energies-and-5-movements-of-taijiquan/

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.

太極拳 is the famous Taoist meditation and martial art exercise. The direct translation of these characters would be something like “grand ultimate fist,” but that does not quite hit the mark for what this title really means.

An early-morning walk through any city in China near a park or an open area will yield a view of Chinese people practicing this ancient technique.

A typical scene is an old man of no less than 80 years on this earth, with a wispy white beard and perhaps a sword in one hand. He makes slow moves that are impossibly smooth. He is steady-footed and always in balance. For him, time is meaningless and proper form, and technique is far more important than speed.

For the younger generation, faster moves may look impressive and seem smooth to the casual observer. But more discipline and mental strength are needed to create perfectly smooth moves in virtual slow motion.

Note: There are two ways to Romanize these Chinese characters, as seen in the title above. The pronunciation and actual characters are the same in Chinese. If you really used English sounds/words to pronounce this, it would be something like “tie jee chew-on” (make the “chew-on” one flowing syllable).

太极拳法 literally translates as “Tai Chi Fist Law” though 拳法 is also known in Japanese as “Kempo” which is sometimes read as “boxing” depending on context.

鐵拳 is a common theme used by various schools of martial arts.

鐵 means “iron” but, in some cases, can mean “indisputable.”
拳 means fist.

Some schools use the older/Taiwanese way to Romanize the iron fist, so you may have seen it spelled “Tieh Chuan” instead of “Tie Quan.” Neither way is technically incorrect.

Note that in Mandarin, the first part of the first character sounds like the English word “tea,” blending into a soft “-eh” sound. The second character sounds a lot like “chew on” but as if it is one syllable.

After WWII in Japan, the Kanji for iron was simplified. This new Kanji form is shown to the right. If you want this modern Japanese version, please click on the Kanji to the right, instead of the button above. The characters shown to the left would still be considered the old or ancient Japanese version of this title.

五形拳 is “Wu Xing Fist” or “Five Form Fist.”

The forms refer to Dragon, Snake, Tiger, Crane, and Leopard.

This term is used in Kung Fu, and is recognized by both Chinese and Japanese practitioners of martial arts.