Karate is a Japanese word, and depending on which kanji you use to write it can mean either "China Hand" or "Empty Hand." The suffix do, meaning "The Way," was added by Funakoshi Gichin (the founder of Shotokan). When the Koreans opened their schools, they naturally spoke Korean. Therefore, they simply translated the word Karatedo into their native language. "The Way of the Chinese Hand" became Tang Soo Do, and "The Way of the Empty Hand" became Kong Soo Do. Some schools also used the term Kwon Bup, the Korean translation of Kempo and a reference to the Chinese art of Ch'uan Fa or "Fist Law." The individual schools themselves were known as Kwans, so therefore you had schools such as Chung Do Kwan Tang Soo Do, or the "Blue Wave School of the Way of the Chinese Hand." Five original Kwans sprang up prior to the Korean War, and an additional four were created before the Korean government forced the Kwans to unify and the term Taekwondo was coined.
Now that I got that out of the way, let's talk about what Korean Karate truly is.