My signs and advertisements do not use the term "Karate," and I politely correct and inform the public, students, parents, and the media when the make the common mistake of confusing the two. Although I have Black Belt rank in a few Japanese and Chinese systems, including Karate, my major is Taekwondo, and that is what I teach.
I see similarities in all physical combative systems, from wrestling and boxing, to Karate, Kung Fu and Taekwondo. I also see similarities in many religions schools of philosophy, scientific research, and artistic expressions in a variety of mediums. Nature provides a common ground, and the human experience provides distinct perspectives, motives, and personal preferences.
I do not believe that Taekwondo came from Karate. I can not analyze the nature of Taekwondo, nor describe its origins based solely on technique, nor on forms (Poomsae/Kata). I call what I do Taekwondo, because I study and teach something that is unique to the Korean culture, and national history, and "Taekwondo" is what they chose to call it upon the suggestion of General Choi Hong Hi.
The Chung Do Kwan that I teach is one of the many sources that bonded together to manifest into the modern Korean Martial Art which we call Taekwondo, yet the founder of Chung Do Kwan, GM Won Kuk Lee, was teaching a system which differed from the Karate that he had learned from Gitchen Funakoshi. Although the Chung Do Kwan, like many of the Kwans, eventually embraced and accepted the use of the term Taekwondo, they did not change to mold their system of teaching after General Choi since others were older, higher rank, and senior to Choi. The Karate influence in these people's lives is evident, and the borrowing of forms practice as a framework for practicing "Taekwondo technique" post WWII is obvious, and absolute. However, Taekwondo became the melting pot of all of Korea's ancient fighting tactics, philosophies, strategy, and cultural identity that did not exist outside of Korea.
My definition of a "Martial Art" goes beyond the modern over-simplification of any, and all combative fighting skills. I only apply the term to Self Defense oriented tactics that are based in advanced scientific principles, and coupled with a life altering education of enlightened philosophy, with high moral and ethical principles. Karate and Taekwondo fall under the same heading of "Martial Art," when taught correctly, but differ in technical applications, fight strategy, development of power, and deep rooted philosophies originating in two different countries.
Not necessarily the "right" answer, but my answer. 
Chief Master Darwin J. Eisenhart
