剛柔流 is the title of the Goju-Ryu or Gōjū-Ryū school/style of Karate or Japanese martial arts.

Sometimes romanized as Gojo-Ryu or Gojoryu, though technically, it should be Gōjū-Ryū (the accents indicating long vowel sounds like “gou juu ryuu”).

不動心流 can be translated as “Fudoshin-Ryu,” or “Immovable Mind Style.”

大東流 is Daitō-ryū, a Japanese martial art style - usually associated with Aikido.

玄制流 is the Japanese title for the Genseiryū or Gensei-Ryū style of Karate.

上地流 or Uechi-Ryū is the short name for a traditional style of Okinawan karate.

Uechi-Ryū is named after its creator, Kanbun Uechi. Uechi was an Okinawan man who left at the age of 19 for China to study Chinese martial arts and medicine.

The meaning of this title is “Uechi Flow,” “Uechi Style,” or “Uechi School.” Although, the name 上地 or Uechi can mean “higher stages of practice” in the Buddhist context. Therefore, you can stretch the meaning to be “Higher-Stages-of-Practice Style.”

少林寺流 is the Japanese martial arts title “Shorin-ji-ryu.”

Though the first part of the title comes from the Shaolin temple in China. In Japan, this refers to an Okinawa school of karate.

Note: Sometimes, this title is written without the “ji” or “temple” Kanji.

無雙直傳英信流 is the traditional or old way to write the Japanese martial arts title, Musō Jikiden Eishin-Ryū (iaido style).

In modern Japanese, the second and fourth Kanji are different, making them 無双直伝英信流.

Musō Jikiden Eishin-Ryū is arguably the most renowned Japanese sword art school, with a history dating back to the early 1600s.

大東流合気柔術 is Daitō-Ryū Aiki-jūjutsu, a Japanese martial art established by Takeda Sōkaku.

The most famous student of Daitō-Ryū Aiki-jūjutsu is Morihei Ueshiba who later founded the school or branch of martial arts known as Aikido.

Note: 大東流合気柔術 can also be romanized as Daito-ryu Aiki-Jujutsu, Daitou-Ryuu Aiki-Juujutsu or Daito-Ryu Aiki-Jujitsu.

無双直伝英信流 is the modern way to write the Japanese martial arts term, Musō Jikiden Eishin-Ryū (iaido style).

Sometimes the second Kanji is written as 雙, and the fourth Kanji is written 傳, making the full title 無雙直傳英信流. See the other version of this title if you want that traditional version.

Taidō (The Way of the Body) is a style of Karate practiced in Japan and popular worldwide.

Taidō or 躰道 traces a lineage from Genseiryū (玄制流), which came from Shuri-te (首里手), one of the original martial arts schools of ancient Okinawa.

The first character 躰 is a variant of the original Chinese character 體. In modern Japan, they tend to use 体, a more simple character form. 体 is also the modern Simplified Chinese form of 體.
The 躰 character is correct for this 躰道 martial arts title. But it can be confusing with so many variants out there, not to mention other homophonic Japanese words that also romanize as Taidō or Taidou.

To have a bit more fun with this 躰 character, it has a 身 radical on the left, which sets it apart. The meaning doubles up on the “body” as 身 (shin) is a character that also means body in Japanese and Chinese. On the right is 本, which often means root, stem, origin, source, or fundamental (but can also mean “book” in some contexts). This has deviated from the original 體 which was 骨 (bone) + 豊 (vessel). Hence, the body was your “bone vessel” in ancient Asia.

The meaning of 躰, as well as 體 and 体, is usually translated as the body. When related to the physical body, it can also refer to the torso, trunk, build, physique, or the constitution of a person. As an extension of this, it can also refer to someone's health (good body = good health).
However, depending on the context, it can encompass other meanings such as form, style, system, experience, aspect, corpus, corporeal, substance, or essentials.

The second character, 道, is recognized and well-known as the “Way” and is the same “do” as in Karate-do or Aikido.

小林流志道館 is the Japanese title Shorin-ryu Shidōkan.

糸東流氣目館空手道 is the title for Shito-Ryu Ki-Me-Kan Karate-Do.
A school of Karate.

Note that while this title can be pronounced in Chinese, it only makes complete sense in Japanese.