You bow. That's it.
there are many different types of karate and they are all created by different people
there are no such things as jujitsu karate
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There is no "Plain Karate." Karate originated in Okinawa. It has spread throughout the world. It has been modified in many places and there is what is often referred to as Japanese Karate, Korean Karate and even American Karate. They all incorporate aspects of the original styles from Okinawa, and incorporate local martial arts as well.
Sport karate is geared towards competition rather than as a martial art. Budō is simply a Japanese word for martial arts, with gendai budō referring to styles that came about after the Meiji restoration - karate, aikido, judo, kendo etc. As such ALL karate is "budo karate".
There are different things to learn at different places
There is only one known on the east coast; Soke Tony Morrison.
As far as I know (from listening in karate class) martial arts started in China and were brought to Japan along with calligraphy and art. However, the stereotypical, "karate" (there are many many different forms) was "invented" in Japan.
They are different, but closely related. Taekwando is a combination of the Ancient arts of Korea combined with karate from Japan. And the Japanese got the art from Okinawa. Many of the kata in taekwando can be identified from their origins on Okinawa.
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