Differences between Japanese Karate roundhouse kick and the Korean Taekwondo round/turning kick
In the karate roundhouse kick, the knee is lifted, the hip is turned over, and the leg is snapped outward from the knee to deliver a strike with the ball of the foot; the support heel rotates about 90 degrees toward the target. Masutatsu Oyama modified the kick in Kyokushin karate by using the instep or shin instead of the ball of the foot as the striking point, using more hip rotation, and by shifting the body mass into the target to create a bludgeoning type of strike.
The Muay Thai roundhouse kick is a bit different from the karate version. The kicker raises on the ball of the supporting foot to generate greater turning speed. The power comes from the pivoting of the hips and the spin more than from a snapping of the leg, which stays relaxed during the kick. Because the kick is executed with so much speed and power, a missed kick causes the kicker to keep spinning. The Muay Tai roundhouse kick uses the shin as the striking area.
Initially, the Taekwondo roundhouse kick was the same as the karate roundhouse kick, but, as Taekwondo began trying to rid itself of its Shotokan influences, the kicks began to differ. In the Karate roundhouse kick, the supporting foot pivots about 90 degrees toward the target, which means the kicking foot travels in a quarter of a circle. Taekwondo instructors theorized that, if you pivot the support foot 180 degrees, more body mass would be imparted to the kick since the kicking foot would travel in a half circle instead of a quarter circle.
Since Gen. Choi's Taekwondo was designed for the military, the round kick was designed to be used while wearing combat boots, so the toes did not have to be curled back. Instead, the point of the shoe was purposed used. With the full pivot of the body, swinging of the leg, and chambering of the lower leg backward, and then snapping it out, and back to the chamber position in a whip-cracking motion , much power is imparted to the small impact point at the point of the boot. When kicking barefoot, the toes must be curled back so the impact point is the ball of the foot. After rise of the Olympic sport style of Taekwondo, there were a lot of complaints about the "slow speed" of the round kick and toe injuries from kicking training bags with the ball of the foot, so a different type of round kick was developed. A knee whip motion with an impact that pushes beyond the target was developed. This was further aided by the in-stepping and kicking at 45 degree angle. This 45 degree round kick was used in the traditional Taekwondo, as in the Choong Moo pattern, but was not used much in sparring.
Therefore, there are two types of round kicks in Taekwondo. The old, traditional style and the new, modern style (bit chagi). Both of which are different from the karate "mawashi geri" roundhouse kick.