柔術 has been somewhat incorrectly spelled and pronounced “Jujitsu” for some time in the English-speaking world. The correct Japanese Romaji is Jujutsu or Juujutsu.

A little background on the word: By combining the Kanji pronounced “Ju” (which means flexible, pliable, gentle, yielding) with the Kanji pronounced “Jutsu” (which means art or technique), we get a meaning that can be translated as “flexible technique,” “gentle art” or “yielding technique.”
柔術 does make sense in Chinese as well, although pronounced “rou shu” in China.

The Jujutsu system has a history in Japan that started well before the 1600s. Some see this style as a variation of the “Empty Hand Method” (Karate-do). Even the samurai of old used some Jujutsu methods in defending themselves with their unarmed hands against weapons that could pierce their heavy armor.

There are convoluted relationships between various schools and systems of martial arts, but it's generally accepted that Jujutsu led to the development of Judo and a few other variations.

Hapkido or 合氣道 is a mostly-defensive martial art in Korea.

Hapkido has some connection to the Aikido of Japan. They are written with the same characters in both languages. However, it should be noted that the Korean Hanja characters shown here are the traditional Chinese form - but in modern Japan, the middle character was slightly simplified.
Note: You can consider this to be the older Japanese written form of Aikido. Titles on older books and signs about Aikido use this form.

The connection between Japanese Aikido and Korean Hapkido is muddled in history. The issue is probably due to the difficult relationship between the two countries around WWII. Many Koreans became virtual slaves to the Japanese during that period. After WWII, many things in Korea were disassociated from having any Japanese origin. The relationship has greatly mellowed out now.

Looking at the characters, the first means “union” or “harmony.”
The second character means “universal energy” or “spirit.”
The third means “way” or “method.”
One way to translate this into English is the “Harmonizing Energy Method.” This makes sense, as Hapkido has more to do with redirecting energy than fighting strength against strength.

More Hapkido info

More notes:
1. Sometimes Hapkido is Romanized as “hap ki do,” “hapki-do” “hab gi do” or “hapgido.”

2. Korean Hanja characters are actually Chinese characters that usually hold the same meaning in both languages. There was a time when these characters were the standard and only written form of Korean. The development of modern Korean Hangul characters is a somewhat recent event in the greater scope of history. There was a time when Chinese characters were the written form of many languages in places known in modern times as North Korea, South Korea, Japan, Vietnam, Singapore, Hong Kong, Taiwan, Mainland China, and a significant portion of Malaysia. Even today, more people in the world can read Chinese characters than English.

3. While these Korean Hanja characters can be pronounced in Chinese, this word is not well-known in China and is not considered part of the Chinese lexicon.