Shotokan is the original form brought to mainland japan from okinawa by funikoshi. It basically incorporates linear movement and utilizes the theory of one strike = one kill. This is why in traditional shotokan karate tournaments there is a point system and the action is stopped after a clean technique/strike has landed. Kyokushin was created by masatatsu oyama, a student of funikoshis. He found that the best way to train was with full contact strikes and to not stop after a clear technique had landed, as it was more realistic.
Kyokushin is really the genesis for japanese kickboxing and thats why a guy like GSP will stand and trade while a guy like Machida prefers to land pin point strikes at a time.
Machida is traditional shotokan karate as his father is a 5th degree black belt in the JKA (japanese karate association).