Kyokushin have several different roundkicks.
The basic one, is very similar to muaythai roundhouse lifting the knee high to the side, but connects with the instep and stops after passing "through" the opponent center line (not spinning all the way through -turning the kicker in a circle like a full muaythai kick. Doing it that way is called "kaiten mawashi geri" and is also taught in kyokushin). The way you focus or stop, the kick often gives it a "snap".
That however is just the most basic version, and other versions using the Shin, and even the ball of the foot follow -ive even been shown a version doing it with the point of the toes, like in some okinawan styles. But was also warned that doing it that way was begging to break your toes and losing the fight. Then there are many other variations such as the "kyokushin kick" or "brazilian kick" (it has many names -even more so in japanese). It has a very "snappy" apperance.
Even the standard point karate snapping roundkick (lifting the knee straight forward and snap it into a roundkick from there) are taught among the "extra" techniques, but it is seldom used.
