I have to disagree here. Taekwondo and Karate are intimately tied. A brief history lesson:
Prior to the Japanese occupation of Korea, native martial arts like Hwarang-Do and other combative practices were quite prevalent. Buddhism had taken a firm hold in Korea, so the influence of Chinese martial arts was undeniable. NONE of these native Korean arts resembled TKD.
When Japan occupied Korea, all native martial arts were banned. During this period, Karate was proliferated throughout the Korea nation. So much so that Koreans began to develop their own, "new," modern martial art known writ large as Tang Soo Do, or, "The Way of the China Hand." For those who are well informed, the Chinese characters which represented the word Karate in Japan originally meant "The Way of the China Hand."
The Japanese latered altered the Kanji and changed the its meaning to "Empty Hand" for nationalistic purposes, and to distance the art its Chinese origins.
So now, we have Tang Soo Do and Karate. For all intents and purposes Tang Soo Do was/is Karate taught by Korean masters. Looking at the forms alone, the similarities between TSD and the Shotokan School of Karate are remarkable. There is atleast a 90% overlap in the forms.
After WWII and the deoccupation, Korean arts flourished. TSD split into numerous Kwans, each master teaching something slightly different. This is why you see the dichotomy between Hee Il Cho's TKD, the Kukkiwon TKD, and Choi's ITF TKD.
Not getting ahead of ourselves here, around the 1950s General Choi met with numerous leaders of the different Kwans and tried to unify the Korean Kwans (still very much "Karate" for all intents and purposes) into a single Korean art - Taekwondo. Unfortunately, politics and internal conflict caused a further rift, and the Kwans remained largely disparate.
The major evolution of Korean arts came with the development of Kukkiwon. Here, new forms were created and the definitive "Korean"-ness came into play. Olympic competition was a goal from the beginning for the WTF, which was largely an extension of Kukkiwon. In contrast, General Choi's forms were the byproduct of he himself, while Kukkiwon came from a meeting of numerous masters.
Unfortunately, the "Palgwae" poomse were slopped together in two weeks time, with the ultimate intention of making TKD "look" different from Karate. By the 70s however, the art had changed significantly. The development of the Taegeuk poomse shortened stances and emphasized the new kicking slant brought into TKD, with full-contact sparring taking the focal point of the art.
Something to note - prior to Korean influence, Karate practitioners were not throwing spinning heel kicks, spinning round kicks, or any of the more advanced kicking techniques taught today. This was a large byproduct of the Korean influence. There has been an extensive cross proliferation of techniques between Karate and Taekwondo.
Today you can find Tang Soo Do schools that teach something very akin to what TKD looked like before its evolution. The particular Kwan TSD evolved from (Moo Duk Kwan) also has a TKD arm. Some Moo Duk Kwon masters refused to join Kukkiwon and the TKD banner, thus retaining the older techniques.
ITF schools are harder to find. Recently a major split occurred in ITF due to the passing of General Choi. The forms of ITF utilize a "wave" motion and keep the longer stances of Karate. Kukkiwon (or "WTF" TKD) is the TKD we all know and most people lambast today. Most schools teach only the sport aspect of TKD.
Much like Muay Thai, which has an extensive traditional lineage, only the techniques applicable in competition are taught.
So, to say the TKD is not Karate is a misnomer. TKD, I would argue, is as much Karate as any of the native Japanese or Okinawan arts. Feel free to disagree, but given the historical circumstances, I feel that ignoring TKD's evolution from Japanese Karate is ignoring the very firmament of the art itself.
I've been a TKD practitioner for 9 years. One of the requirements of receiving a black belt was the recitation of a fairly extensive history of TKD. In this, the dogma of TKD as a "3000 year old art" was central to the theme. I wish the powers that be in TKD would accept the fact that TKD is a modern martial art, and has little tie (in its current incarnation) to anything beyond the integration of Japanese Karate.
That said, TKD is a great, physical art. Far more demanding physically than any traditional Karate, I feel like at a young age TKD may be the way to go.